Kelowna, and to UBC's Okanagan campus. - CUMC - Canadian ...

The Canadian Undergraduate 

Mathematics Conference 

2012 

Congrès Canadien des Étudiants en 

Mathématiques 

July 11-15 juillet 2012 

The University of British Columbia’s 

Okanagan Campus 

Kelowna, British Columbia

Contents 

1 Committee Notes 4 

1.1 Welcome / Bienvenue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

1.2 Welcome From Studc / Un message de Studc . . . . . . . . . . . . . . . . . . . . . . 5 

1.3 Committee Bios / Biographies des membres du comité . . . . . . . . . . . . . . . . . 7 

1.4 Attendee Policy / Politique de participation . . . . . . . . . . . . . . . . . . . . . . . 12 

2 Schedule of Events 14 

2.1 Basic Schedule / Horaire de base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

2.2 Comprehensive Schedule / Horaire de compléter . . . . . . . . . . . . . . . . . . . . 16 

2.3 Activities / Activités . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

3 Abstracts / Résumés 25 

3.1 Keynote Abstracts / Résumés plénière . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

3.2 Student Abstracts / Résumés des étudiants . . . . . . . . . . . . . . . . . . . . . . . 28 

4 General Information / Informations générales 64 

4.1 Internet connections on campus / Connexions Internet sur les campus . . . . . . . . 64 

4.2 Getting to/from Okanagan College and the closing banquet . . . . . . . . . . . . . . 65 

4.3 Kelowna transit information / Le transport en commun á Kelowna . . . . . . . . . . 67 

4.4 Great places to eat in Kelowna / Bons endroits où manger à Kelowna . . . . . . . . 69 

4.5 Fun things to do in Kelowna / Activités amusantes à Kelowna: . . . . . . . . . . . . 70 

4.6 CUMC 2013 Host Bids / Enchères pour accueillir le CCÉM 2013 . . . . . . . . . . . 72 

4.7 Sponsors / Commanditaires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 

4.8 Riddles and Games / Énigmes et Jeux . . . . . . . . . . . . . . . . . . . . . . . . . . 78 

4.9 Campus Maps / Cartes du campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

3

Committee Notes 

1.1 Welcome / Bienvenue 

Welcome to the 19th annual Canadian Undergraduate Mathematics Conference! This year we are 

proud to present to you seven keynote speakers, in addition to the 86 student talks from over 25 

different universities and colleges from across Canada and the USA. 

UBC’s Okanagan campus aims to be ecologically friendly by focusing on sustainability through- 

out our campus. One of the ways we accomplish this is by being bottled water free; please 

make use of the reusable water bottles we have provided for you and the water stations in var- 

ious buildings. As well, please take note of the waste receptacles all around campus which are 

labelled for recyclable materials, returnable bottles, and other wastes. Please help keep our cam- 

pus and environment clean and healthy. For more information on our sustainability programs see 

www.ubc.ca/okanagan/sustainability. 

The CUMC is a unique opportunity for you to share ideas and make connections that could last 

you a lifetime. We know that you will be inspired by the talks you listen to and the people you 

meet this week. Enjoy your time here and welcome to beautiful Kelowna, BC! 

Bienvenue 

Bienvenue au 19e Concrès Canadien des Étudiants en Mathématiques! Cette année, nous sommes 

fiers de vous présenter sept conférences plénières, en plus des 86 présentations étudiantes de 25 

universités et collèges de partout au Canada et aux États-Unis. 

Le campus Okanagan de l’UBC a pour objectif d’être écologiquement responsable, en se con- 

centrant sur la durabilité à travers tout le campus. L’une des façons d’accomplir cet objectif est de 

supprimer les bouteilles d’eau; nous vous prions donc de vous servir des bouteilles réutilisables que 

nous vous avons fournies, ainsi que des fontaines à eau disponibles dans plusieurs bâtiments. De 

plus, vous remarquerez que les poubelles sur le campus permettent le tri des matériaux recyclables, 

des bouteilles recyclables et des autres déchets. Nous vous serions gré de nous aider à garder notre 

4

1.2. WELCOME FROM STUDC / UN MESSAGE DE STUDC 5 

campus et notre environnement propres et sains. Pour plus d’informations sur notre programme de 

durabilité, vous pouvez visiter le www.ubc.ca/okanagan/sustainability. 

Le CCÉM est une opportunité unique de partager vos idées et de créer des relations qui pour- 

raient durer toute votre vie. Nous savons que vous serez inspirés par les présentations que vous 

écouterez et par les personnes que vous rencontrerez. Nous vous souhaitons un agréable séjour ici, 

et soyez les bienvenus au bel endroit qu’est Kelowna, en Colombie-Britannique! 

1.2 Welcome From Studc / Un message de Studc 

This year, the CUMC turns 19, the legal drinking age in British Columbia, and where better to 

celebrate than in the heart of the province in the beautiful Okanagan Valley famous for its wineries. 

Much like any 19-year-old, the CUMC constantly changes: each year, participants and organizers 

bring the conference its unique flavour - from the crisp, sophisticated notes of Ontario to the bright, 

expressive aromas of Quebec to the mellow, luscious bouquet of the West coast. Throughout all this 

change and throughout all these years, what keeps the CUMC going is the enthusiasm of everyone 

involved. As the overseeing body, the CMS Student Committee (Studc) shares the excitement and 

the passion of the organizers; we are happy to see the conference evolve - it supplies us with new 

ideas and influences our own projects. Studc not only ensures the continuation of the CUMC, 

it also supports regional events, publishes the semi-annual newsletter Notes from the Margin and 

holds students events at the Canadian Mathematical Society’s winter and summer meetings. For 

more information on our past and present projects, check us out on the web at studc.cms.math.ca 

and don’t hesitate to drop us a line at chair-studc@cms.math.caas we are constantly looking for 

feedback. 

This year’s dynamic CUMC organizing team has done an amazing job putting together a great 

event. But it is the participants that make the conference happen, so we strongly encourage you to 

partake in all of this year’s numerous activities. Whether on the wine tour with Okanagan’s best 

or at breakfast with some OJ, I invite you to raise the glass in celebration of CUMC 2012. 

Un message de Studc 

Cette annèe, le CCÉM a enfin atteint l’âge légal pour boire en Colombie-Britannique et quoi de 

mieux que de célébrer cet événement au coeur de cette province, dans la magnifique vallée de 

l’Okanagan qui est reconnue pour ses vignobles. Á l’image des jeunes de 19 ans, le CCÉM est 

bouillonnant de projets. Chaque année, les participants et les organisateurs apportent leurs saveurs 

particuliéres, en commençant par les notes mordantes et sophistiquées de l’Ontario, aux arômes

6 CHAPTER 1. COMMITTEE NOTES 

expressifs et éclatants du Québec en passant par la tranquilité teintée d’extravagance de la côte 

Ouest canadienne. 

À travers le temps et les changements, ce qui tient en vie le CCÉM est certainement l’enthousiasme 

de toutes les personnes impliquées dans levènement. En tant qu’organisation chapeautant le congrès, 

le comité étudiant de la SMC (Studc) partage l’effervessence et la passion des organisateurs. Nous 

sommes heureux de constater que le congrès évolue, nous amenant de nouvelles idées et influenant 

nos projets. En plus d’assurer la continuité du CCÉM, le Studc supporte des événements régionaux, 

publie deux fois par année le bulletin “Notes from the Margin” et organise des activités étudiantes 

aux deux rencontres annuelles de la Société Mathématique du Canada. Pour plus d’informations 

sur nos projets passés et actuels, allez visiter notre site web studc.cms.math.ca et n’hésitez pas á 

nous écrire à chair-studc@cms.math.ca. Nous sommes toujours ouverts aux commentaires. 

Le dynamique comité organisateur de cette année a mis beaucoup d’efforts dans l’organisation 

de ce congrès. Par contre, ce sont les participants qui font en sorte que le congrès est possible et 

c’est pourquoi nous vous encourageons fortement à participer aux nombreuses activités qui s’offrent 

à vous cette année. Que ce soit pendant la tournée des vignobles de la vallée de l’Okanagan ou en 

savourant un bon jus d’orange frais au déjeuner, vous êtes invités à lever votre verre pour célébrer 

le CCÉM 2012.

1.3. COMMITTEE BIOS / BIOGRAPHIES DES MEMBRES DU COMITÉ 7 

1.3 Committee Bios / Biographies des membres du comité 

Figure 1.1: Committee from left to right: Crystal Parras, Jodie Foster, Spencer Hunt, Garrett 

Culos, Andrea Hyde, Rodney Earl and Faisal Rahman. 

Crystal Parras - President 

Crystal Parras is going into her fourth year of BSc Applied Math with Honours at UBC’s 

Okanagan campus. Having first been a hairdresser for ten years, she took a turn into a completely 

different direction and now uses pencils and graph paper as her weapon of choice instead of scissors... 

though who’s to say what would cause more damage! She is looking forward to delving into courses 

on financial math and statistics in the fall, and her goal is to continue this on into graduate studies. 

Crystal is also President of the Math and Stats Course Union, and when she’s not studying, you 

can catch her snowboarding, dancing around to drum ‘n’ bass, cutting her friends’ hair, and just 

being a general nuisance. 

Crystal Parras débute sa quatrième anne d’étude au Baccalauréat en Mathématiques Appliquées 

à l’UBCO. Après avoir travaillé comme coiffeuse durant 10 ans, elle a emprunt une toute autre 

direction et a troqué ses ciseaux pour des crayons et du papier quadrillé. Dans les prochaines 

années elle envisage de s’orienter vers les statistiques et les mathématiques financières dans le but 

de poursuivre des études supérieures. Crystal est aussi Présidente du Math and Stats Course Union 

et lorsqu’elle n’étudie pas, elle aime faire de la planche à neige, danser au son du drum n bass et 

couper les cheveux de ses amis.


Andrea Hyde - VP Logistics 

Andrea Hyde completed her BSc in Math with Honours at UBCO this year. Her undergraduate 

work was in Mathematical Biology under the supervision of Dr. Rebecca Tyson. She is excited to 

begin her MSc this fall in Number Theory with Dr. Blair Spearman at UBCO. Andrea is also the 

Internal Co-ordinator for the Math and Stats Course Union on campus. When not being a terrible 

nerd, Andrea loves biking, snowboarding, drinking beer with friends, and cuddling with her dogs. 

She highly recommends that you have the all you can eat waffles at the Jammery while you’re here. 

Andrea Hyde vient tout juste de compléter son baccalauréat en mathématiques à l’UBCO. Son 

projet d’étude a porté sur la biologie mathématique, sous la supervision de Rebecca Tyson. Elle 

est enthousiaste à l’idée de commencer sa maîtrise à àutomne dans le domaine de la théorie des 

nombres avec Blair Spearman à UBCO. En plus de son implication pour le CCÉM, Andrea est 

Coordinatrice Interne du Math and Stats Course Union. À part être une incroyable ’nerd’, Andrea 

aime faire du vélo, de la planche à neige, boire de la bière avec des amis et jouer avec ses chiens. 

Selon elle, un déjeuner au crêpes-à-volonté du Jammery s’impose lors de votre passage à Kelowna. 

Spencer Hunt - VP Finance 

Spencer has grown up in the Okanagan in the small town of Okanagan Falls (there wasn’t even 

a Tim Hortons!). Throughout his four years at UBC’s Okanagan campus, Spencer has tried to be 

involved with the campus community. Working on campus as a residence advisor, teaching assistant, 

supplemental learning leader, and as the orientation coordinator, has fueled his passion for students 

and helping them succeed. Spencer was also a part of the President’s non-academic misconduct 

committee, where the students would serve as an impartial body to students that have broken the 

campus conduct. Being a part of this committee has encouraged him to attend law school, and 

he will be taking the LSAT later this year. Spencer feels that his education in mathematics will 

provide him the objectivity and analytical skills to succeed on this career path. 

Spencer Hunt a grandi dans le petit village d’Okanagan Falls (où il n’y a même pas de Tim Hor- 

tons!). Pendant ses quatres années sur le campus de UBCO, Spencer s’est impliqué de nombreuses 

faons. Il a travaillé à titre de responsable de résidences, d’auxiliaire d’enseignement et de conseiller 

en orientation, ce qui a alimenté sa passion pour la réussite des étudiants. Spencer a également 

fait partie du President non-academic misconduct committee, dans lequel les étudiants servent de 

corps impartial dans le jugement des étudiants ayant enfreint les lois du campus. Prendre part à 

ce comité l’a encouragé à s’inscrire à l’école de droit et il passera ses examens d’admission dans le 

courant de l’année. Spencer considre que ses études en mathématiques lui ont donné l’objectivité 

et les outils analytiques nécessaires pour réussir dans sa future carrière.


Rodney Earl - VP Logistics 

Rodney Earl is going into his fifth year of his BSc with a double major, one in Computer Science 

and the other in Mathematics, with a concentration in Pure Math. Math has always been a hobby 

of Rodney’s and became more of a passion as he continued his years of study. By the end of his 

second year, he knew that understanding how and why math works was very interesting to him, so 

he decided to take a concentration in the pure side of math. Outside of school, Rodney is a member 

of the Cadet Instructor Cadre, which is a sub component of the Canadian Forces, that specializes in 

the instruction, mentoring and development of youth in the Cadet Program. When not studying, 

working on projects or planning different activities for Cadets, Rodney enjoys reading and hanging 

out with his friends. 

Rodney Earl débute sa cinquième année de baccalauréat avec majeure double en Informatique 

et en Mathématiques. Les mathématiques ont toujoursété un passe-temps pour Rodney et sont 

devenues une passion au cours de ses études. À la fin de sa deuxième année, il savait que la 

compéhension du fonctionnement des mathématiques était de première importance pour lui, ce qui 

l’a mené vers les mathématiques pures. En dehors du cadre scolaire, Rodney est un membre des 

Cadres Instructeurs des Cadets, une organisation affiliée aux Forces Canadiennes qui se spécialise 

dans la formation et le développement des jeunes Cadets. Dans ses temps libres, Rodney aime lire 

et passer du bon temps avec ses amis. 

Jodie Foster - VP Fundraising 

Jodie is entering her final year of a BSc in Mathematical Sciences with a minor in Physics. She 

is greatly looking forward to an awesome last year with her involvement as a teaching assistant in 

Math and Statistics as well as her position as the student coordinator for the Math and Science 

Tutor Centre. Next year she will be starting her MSc in Astrostatistics. In her spare time Jodie 

can be found travelling the world. She has spent time in both Sweden and Bolivia. Jodie also likes 

to spend her time in the Okanagan with friends and family. Fun fact: Jodie’s obsessive love for 

Harry Potter and Star Wars (she owns 12 bobble heads of various characters) has provided her the 

attainment of badass status. 

Jodie débute sa dernière année de baccalauréat en mathématiques avec mineure en physique. 

Elle envisage une superbe année compte tenu de son implication comme auxiliaire d’enseignement 

et comme coordonnatrice étudiante du centre de tutorat. Par la suite, elle compte faire une maîtrise 

en Astrophysiques. Dans ses temps libres, Jodie aime passer du temps dans la vallée de l’Okanagan 

avec sa famille et ses amis. Fait cocasse: L’obsession de Jodie pour Harry Potter et Star Wars


(elle possède 12 bobble heads de diffrents personnages) est la seule chose qui l’empêche d’obtenir le 

statut de “badass”. 

Faisal Rahman - Web Coordinator 

Faisal Rahman started his academic career with an obsession for Machine Learning and Artificial 

Intelligence, but slowly his passion grew for Mathematics. He feels blessed to be able to see the 

beauty of Mathematics behind equations. While he has his weakness for theoretical mathematics, 

he also allows himself to explore his affection for other branches of arts and science. His career 

dream is to aid the study of human behavior with mathematics, and possibly extend the research 

to Artificial Intelligence. He enjoys dancing, sports, and looking at paintings. He gets inspired by 

the success of others, and always inspires others to reach their potential. His true inspiration is 

Salman Khan, who in his graduation speech said, “It is no exaggeration to say that we will change 

the world”, and later formed the Khan Academy, which helps educate millions of people. 

Faisal Rahman a dèbuté sa carrière académique avec une obsession pour l’intelligence artifielle et 

l’apprentissage automatique, puis sa passion pour les mathématiques s’est graduellement dévelop- 

pée. Il se considère chanceux de saisir la beauté des mathématiques au-delà des équations. Même 

si les mathématiques théoriques le captivent, il aime explorer d’autres branches des arts et des 

sciences. Dans sa future carrière, il voudrait étudier le comportement humain grâce aux mathéma- 

tiques et peut-être même poursuivre ses recherches dans le domaine de l’intelligence artificielle. Il 

aime la danse, les sports et les peintures. Il est inspiré par le succès de ses collègues et inspire les 

autres à atteindre leur plein potentiel. Il puise son inspiration dans Salman Khan, qui a dit dans 

son discours de graduation que “ce n’est pas de l’exagération de dire que l’on va changer le monde” 

et qui a fondéla Khan Academy, qui aide à éduquer des millions de personnes. 

Garrett Culos - VP Fundraising 

Garrett Culos is going into his fifth and final year at UBC’s Okanagan, where he is studying 

applied math and physics. He will be ending his undergraduate degree by undertaking two honours 

projects specializing in mathematical biology and theoretical physics. When Garrett is not studying, 

he enjoys going to the gym where he picks things up and puts them down. Garrett is a tall man, 

who finds pleasure in playing video games such as Starcraft, Diablo, and Fallout 3. Garrett also 

enjoys long walks on the beach, going to the park to do acrobatic yoga, and talking in the third 

person. If there’s one thing that Garrett stresses most about Kelowna is to bask in the glory that 

is the Wood Fire Bakery and enjoy their succulent chicken cordon bleu. 

Garrett Culos amorce sa cinquième et dernière annèe á l’UBCO où il étudie les mathématiques 

et la physique appliquées. Il terminera ses études de premier cycle avec deux projets d’envergure


en biologie mathématique et en physique théorique. Mis à part l’école, Garrett aime s’entraîner au 

gym où il lève de la fonte. Garrett aime aussi jouer à des jeux tels que Starcraft, Diablo et Fallout 

3. Il aime aussi les longues marches sur la plage, aller au parc faire du yoga acrobatique et parler 

à la troisième personne. S’il pouvait insister sur une chose à faire à Kelowna, ce serait de profiter 

du temps au Wood Fire Bakery en savourant leur poulet cordon bleu.


1.4 Attendee Policy / Politique de participation 

The Canadian Undergraduate Mathematics Conference 2012 is dedicated to providing a harassment- 

free conference experience for everyone, regardless of gender, sexual orientation, disability, physical 

appearance, body size, race, religion, language, or mathematical preference. We do not tolerate 

harassment of conference participants in any form. Sexual language and imagery is not appropriate 

for any conference venue, including talks. Conference participants violating these rules may be 

sanctioned or expelled from the conference without a refund at the discretion of the conference 

organizers. 

Harassment includes: offensive verbal comments related to gender, sexual orientation, disability, 

physical appearance, body size, race, or religion; sexual images in public spaces; following, stalking, 

deliberate intimidation, unwelcome photography or recording; sustained disruption of talks or other 

events; and inappropriate physical contact, or unwelcome sexual attention. Participants asked to 

stop any harassing behavior are expected to comply immediately. 

If a participant engages in harassing behavior, the conference organizers may take any action 

they deem appropriate, including issuing a warning or removing the offender from the conference 

with no refund. If you are being harassed, notice that someone else is being harassed, or have any 

other concerns, please contact a member of conference staff immediately. Conference staff can be 

identified by coloured Organizer and Volunteer t-shirts. 

Conference staff will be happy to help participants contact campus security or local law en- 

forcement, or otherwise assist those experiencing harassment to feel safe for the duration of the 

conference. Campus security can provide escorts if desired. We value your attendance. 

If you have any questions regarding the policy or its enforcement, please don’t hesitate to contact 

us at the email below. 

CUMC 2012 Organizing Committee E-mail: cumc.2012@ubc.ca 

Campus Security (Emergency): 250-807-8111 

Campus Security (Non-Emergency): 250-807-9236 

On-Campus Accommodation: 250-807-8050 

Police/Fire/Ambulance (Emergency): 911 

RCMP (Non-Emergency): 250-726-3300 

Taxi: 250-861-1111 or 250-212-1212 

Kelowna Crisis Line: 1-888-353-2273 

Okanagan College Security (Non-Emergency): 250-317-2435

1.4. ATTENDEE POLICY / POLITIQUE DE PARTICIPATION 13 

Politique de participation 

Le Congrès Canadien des Étudiants en Mathématiques 2012 s’engage à fournir une expérience de 

congrès exempte de harcèlement pour tous, quels que soient le genre, l’orientation sexuelle, les 

invalidités, l’apparence physique, la taille, la race, la religion, la langue ou les préférences mathé- 

matiques de la personne. Nous ne tolérerons le harcèlement de participants au congrès d’aucune 

forme. Le langage et les images à caractère sexuel ne sont appropriées ni lors des conférences ni 

lors des présentations. Les participants aux conférences contrevenant á ces règles pourront être 

sanctionnés ou expulsés des conférences sans remboursement, à la discrétion des organisateurs. 

Le harcèlement inclut : les commentaires verbaux offensifs liés au genre, à l’orientation sex- 

uelle, aux invalidités, à l’apparence physique, à la taille, à la race, à la religion, à la langue ou 

aux préférences mathématiques; l’affichage d’images sexuels dans les espaces publics; le harcèle- 

ment criminel, la traque, l’intimidation délibérée, les photographies ou enregistrements déplacés; 

des interruptions soutenues de présentations ou d’autres événements et des contacts physiques in- 

appropriés ou une attention sexuelle importune. Les participants à qui l’on demandera d’arrêter 

tout comportement d’harcèlement devront se conformer aux demandes immédiatement. 

Si un participant se livre à un comportement de harcèlement, les organisateurs des conférences 

pourront prendre toutes les mesures qu’ils jugeront appropriées, y compris émettre un avertissement 

ou retirer le délinquant du congrès sans remboursement. Si vous êtes harcelés, remarquez que 

quelqu’un est harcelé, ou avez connaissance de tout autre renseignement pertinent, nous vous serions 

gré de contacter un membre du personnel (organisateurs ou bénévoles) immédiatement. Ils peuvent 

être repérés grâces aux t-shirts colorés. 

Les membres du personnel seront heureux dider les participants à contacter la sécurité du 

campus, ou le bureau de loi local, ou dider ceux qui subissent le harcèlement à se sentir en sécurité 

pour toute la durée du congrès. La sécurité du campus peut aussi fournir des escortes si nécessaire. 

Nous tenons à votre présence et à votre sécurité. 

Pour toute question concernant la politique ou son application, n’hésitez pas à nous contacterà 

l’adresse de courriel électronique ci-dessous. 

Comité d’organisation du CCÉM: cumc.2012@ubc.ca 

Sécurité du Campus (Urgences): 250-807-8111 

Sécurité du Campus : 250-807-9236 

Hébergment sur le Campus: 250-807-8050 

Police/Pompiers/Ambulance (Urgences): 911 

GRC (Sans urgence): 250-726-3300 

Taxi: 250-861-1111 or 250-212-1212 

Ligne de crise de Kelowna: 1-888-353-2273 

Sècurité du College Okanagan (Sans urgence): 250-317-2435

Schedule of Events 

2.1 Basic Schedule / Horaire de base 

Wednesday July 11, 2012 - Mercredi 11 juillet 

13:00 Check in / Enregistrement 

15:30 Refreshments / Pause café 

16:00 Opening Remarks / Discours d’ouverture 

17:00 Keynote Speaker / Conférence plénière - Tim Swartz 

18:30 Opening Banquet / Banquet d’ouverture 

Thursday July 12, 2012 - Jeudi 12 juillet 

9:00 Student Talks / Conférences étudiantes 

11:00 Coffee Break / Pause café 

11:30 Keynote Speaker / Conférence plénière - Heinz Bauschke 

12:30 Lunch / Dîner 

14:00 Student Talks / Conférence étudiantes 


15:30 Keynote Speaker / Conférence plénière - Donovan Hare 

17:00 Wine Tour (Optional Activity) / Tournée vinicole (Activité facultative) (section 2.3) 

20:00 Movie Night (Optional Activity) / Soirée cinéma (Activité facultative) (section 2.3) 

Friday July 13, 2012 - Vendredi 13 juillet 

7:45 Buses to Okanagan College / Transport vers Okanagan College (see section 4.2) 

8:50 Opening Remarks from Okanagan College / Discours d’ouverture du Okanagan College 



11:30 Keynote Speaker / Conférence plénière - Jennifer Hyndman 

14

2.1. BASIC SCHEDULE / HORAIRE DE BASE 15 




16:30 Keynote Speaker / Conférence plénière - Catherine Beauchemin 

17:30 CUMC 2013 Host Bids / Enchères pour accueillir le CCÉM 2013 ( section 4.6) 

18:30 Women in Math and Science Dinner (Optional Activity) / Souper pour les Femmes en Maths 

et Sciences (Activité facultative)(see section 2.3) 

18:30 Scandia (Optional Activity)/(Activité facultative)(see section 2.3). 

Saturday July 14, 2012 - Samedi 14 juillet 



11:30 Keynote Speaker / Conférence plénière - Dominikus Noll 




15:30 Keynote Speaker / Conférence plénière - Gerda de Vries 

17:30 Closing Banquet / Banquet final 

19:45 Announcement of CUMC 2013 Host University / L’annonce de l’université d’accueil CCÉM 

2013 

Sunday July 15, 2012 - Dimanche 15 Juillet 

Free day to tour Kelowna/ Journée libre pour visiter Kelowna

16 CHAPTER 2. SCHEDULE OF EVENTS 

2.2 Comprehensive Schedule / Horaire de compléter 

Wednesday July 11, 2012 - Mercredi 11 juillet 

Time - Heure Description Room - Local 

13:00 - 15:30 Check in / Enregistrement Fipke Foyer 

15:30 - 16:00 Refreshments / Pause café Fipke Foyer 

16:00 - 16:20 Opening Remarks / Discours d’ouverture Fip 204 

16:20 - 17:00 Carolyn Labun - How to Make Your Conference Presentation 

Count 

17:00 - 18:00 Keynote Speaker / Conférence plénière : Tim Swartz - 

Statistical Excursions in Sport 

Fip 204 

Fip 204 

18:30 - 20:30 Opening Banquet / Banquet d’ouverture The Commons 

Thursday July 12, 2012 - Jeudi le 12 juillet 

(behind the 

UNC) 


9:00 - 10:00 

10:00 - 10:30 

Ruth, William - Introduction to Estimation Fipke 124 

Simard, Nicolas - Euclid‘s Elements and Pythagoras’ Theorem Fipke 138 

Baker, Michael - Special Functions and Orthoganal Polynomials Fipke 121 

Tawfik, Selim - Parallel Parking with Lie Algebras Fipke 140 

Raymond-Beizile, Léo - Causal inference and Bayesian propensity 

score adjustment methods 

Fipke 250 

Marceau, Jean-François - Introduction to Additive Frieze Patterns Fipke 129 

Hyde, Andrea - An Individual Based Model for Bear Movement Fipke 124 

Poelstra, Andrew - On the Existence of Double Arithmetic Pro- 

gressions 

Fipke 138 

Beckett, Mathew - Scaling Arguments on the Space of Connections Fipke 121 

Mehta, Arthur - The Story of Srinivasa Ramanujan Fipke 140 

Godin, Jonathan - Analysis Around Fractals Fipke 250 

Luther, Robert - Combinatorial Designs and Block-Intersection 

Graphs 

Fipke 129

2.2. COMPREHENSIVE SCHEDULE / HORAIRE DE COMPLÉTER 17 

10:30 - 11:00 

Banero, Graham - Abelian and Additive Complexity: Analyzing 

Structure in Infinite Words 

Foster, Jodie - Supplemental Learning: A New Way to Learn 

Mathematics! 

Fipke 124 

Fipke 138 

Richards, Larissa - Pattern Subgroups of GLn(F) Fipke 121 

Ryan, Philip - As Easy as A, B, C Fipke 140 

Deschênes, Andréa - Connexions et Calcul Rigourex Fipke 250 

Recoskie, Jeremy - Critical Issues in Statistical and Biological In- 

terperetation 

Fipke 129 

11:00 - 11:30 Coffee Break / Pause café Fipke Foyer 

11:30 - 12:30 Keynote Speaker / Conférence plénière: Heinz Bauschke 

- An invitation to projection methods 

Fip 204 

12:30 - 13:30 Lunch / Dîner Fipke Foyer 

14:00 - 15:00 

Pynn-Coates, Nigel - VC Dimension and Density: Connections 

between Computational Learning Theory and Model Theory 

Hsu, Chieh-Ting (Jimmy) - The Convergence Criterias of the 

Bayesian Monte Carlo Simulation on the Quantification of the 

Number of Fluorophores in a Cell 

Charlesworth, Ian - DFAs, Automatic Numbers, and Transcen- 

dence 

Tarzwell, Caleb - Modelling Techniques of Genetic Information 

Flow: Past and Future 

Fipke 124 

Fipke 138 

Fipke 121 

Fipke 140 

Snarski, Michael - Representations of Harmonic Donuts Fipke 250 

Asad, Reza - Steiner Symmetrizations: Convergence and Rate of 

Convergence 

Fipke 129 


15:30 - 16:30 Keynote Speaker / Conférence plénière: Donovan Hare - 

To All the Graphs I’ve Loved Before 

17 :00 - 20:30 Wine Tour (Optional Activity) / Tournée vinicole (Activité fac- 

ultative) (section 2.3) 

20 :00 - 22:00 Movie Night (Optional Activity) / Soirée cinéma (Activité facul- 

tative) (section 2.3) 

Fip 204 

Meet at UBC-O 

bus loop 

UNC movie the- 

atre


Friday July 13, 2012 - Vendredi 13 juillet 


8:50-9:00 Opening Remarks from Okanagan College / Discours d’ouverture 

9:00 - 10:00 

10:00 - 10:30 

10:30 - 11:00 

du Okanagan College 

Papst, Irena - From Differential Equations to Diphtheria: The 

Mathematics of Infectious Disease Spread 

Candales, Manuel - Cyclotomic Polynomials and Elementary 

Number Theory 

Centre for 

Learning Atrium 

E202 

E207 

Charron, Philippe - Temperley Lieb Algebras E103 

Pelletier, Laurent - Probability and Measure E208 

Szatmari, Simon - Lie Group Methods for Moving Mesh Algo- 

rithms 

Klusowski, Jason - Flows, Branching Numbers, and Percolation 

on Trees 

E212 

E213 

Parras, Crystal - A Brief History of Women in Mathematics E202 

Reimer, Sarah - Lost in Inversion: Conditioning of Spectral Col- 

location Methods 

Horan, Joseph - Qualitative Analysis of Chemical Reaction Net- 

works 

E207 

E103 

Wu, Steven - A Winning Strategy E208 

Tavakoli, Arman - Introducing Uniformly Distributed sequences E213 

Leylan, Richard - The Roots of Flow and Chromatic Polynomials E202 

Hunt, Spencer - Derivative Free Optimization Techniques on a 

series of test functions 

Hunt, Sean - Cooking Howard’s Curry With The Agda Program- 

ming Language 

E207 

E103 

Maheux, Dominique - Introduction aux Méthodes de Schwarz E208 

Dranovski, Anne - Rate of Convergence of Random Polarizations E213 

11:00 - 11:30 Coffee Break / Pause café Centre for 

Learning Atrium


11:30 - 12:30 Keynote Speaker / Conférence plénière: Jennifer Hynd- 

man - Finite Bases of Quasi-equations of Unary Algebras: How 

Few Rules Can We Get Away With? 

Centre for 


12:30 - 14:00 Lunch / Dîner Centre for 

14:00 - 14:30 

14:30 - 15:00 

15:00 - 15:30 

Lévesque, Jean-Sébastien - Brain, Dynamical Systems and Fun! E202 

Street, Colin - Intuition and Probability E207 

Bouchard, Nicolas - Calcul formel et programmation / Program- 

ming computer algebra 


E103 

Gerbelli-Gauthier, Mathilde - Introduction to Modular Forms E208 

Zung, Jonathan - How Topologically Inclined Thieves Split Their 

Spoils 

E212 

Tufts, Julia - Domination Polynomials of Graphs and Their Roots E213 

Jackett, Neal - An Introduction to Topology E202 

Funk, Jacob - Stabilization Time for a Type of Evolution on Bi- 

nary Strings 

E207 

Gervais, Kevin - Introduction à l’Homologie Singuliére E103 

Klassen, Jamie - Representations and Duality with a View To- 

wards Number Theory 

E208 

Petrie, Tara - Math and Art: the Math Behind the Beauty E212 

Josh Holt, Richard Hudson, Bryan Zintel - Exponential Model of 

the Eiffel Tower 

Culos, Garrett - Predicting the Spatial Distribution of an Orchard 

Insect Pest 

Beg, Nikolina - Principal Component Analysis and its Application 

to High Dimensional Data Sets 

E213 

E202 

E207 

Kabir, Ifaz - A Simple proof of the Jordan Curve Theorem E103 

Sequeira, Nigel - Continuous Model Theory and Von Neumann 

Algebras 

E208 

Provost, Alex - A Topological Proof of the Infinitude of Primes E212 

Al-Shaghay, Abdullah - An Irreducibility Criterion of A. Cohn E213


15:30 - 16:00 

Bidart, Rene - What is Understanding? E202 

Crosbie, Kimberly - Finite State Automata and an Intrusion De- 

tection System 

Mack, Richard - Fundamental Theorem of Calculus for Lebesgue 

Integration 

E207 

E103 

Mather, Kevin - Dirichlet Series and Arithmetic Functions E208 

Mandryk, Isaiah - Structure of Neural Networks E212 

16:00 - 16:30 Coffee Break / Pause café Centre for 

16:30 - 17:30 Keynote Speaker / Conférence plénière: Catherine Beau- 

chemin - Virologie in Silico: Cultiver des Infections en Ordina- 

teur (In Silico Virology: Growing Infections in a Computer) 

17 :30 - 18:30 CUMC 2013 Host Bids / Enchères pour accueillir le CCÉM 2013 

18:30 - 20:30 

( section 4.6) 

Women in Math and Science Dinner (Optional Activity) / Souper 

pour les Femmes en Maths et Sciences (Activité facultative)(see 

section 2.3) 

or 

Scandia (Optional Activity)/(Activité facultative)(see section 2.3) 

Saturday July 14, 2012 - Samedi 14 juillet 


Centre for 


Centre for 



9:00 - 10:00 

Tyson, Rebecca - Opportunities in Mathematical Biology for Grad 

Studies 

Peterson, David - Investigating Orthogonal Latin Squares Using 

Universal Algebra 

Dosseva, Annamaria - Galois Theory and the Insolvability of the 

Quintic 

Fipke 124 

Fipke 138 

Fipke 121 

Butson, Dylan - Introduction to Stochastic Calculus Fipke 140 

Arbour, Jean-François - An Overview of Some Elements of Spec- 

tral Geometry. 

Fipke 250 

Park, Hongyoul (Mike) - Diophantine Approximations Fipke 129 

Wiebe, Toban - Game Theory and Evolution Fipke 133


10:00 - 10:30 

10:30 - 11:00 

Yeremi, Miayan - Statistical refinement of astrophysical numerical 

simulations 

Kovesi, Michelle - An Introduction to Machine Learning for Text 

Classification 

Weng, Gwen Yun - The Shortest Introduction to Semidefinite Pro- 

gramming 

Fipke 124 

Fipke 138 

Fipke 121 

Martieau, Joanie - Weyls Theorem Fipke 140 

Reid, Samuel - Simplicial k-Combinatorial and Packings: Touch- 

ing (k + 1)-tuples of Congruent Balls in 3-space 

Davis, Chad - Exploiting Known Structures to Approximate Nor- 

mal Cones 

Lyon, Keenan - Using Symmetry Groups to Solve Partial Differ- 

ential Equations 

Dhawan, Andrew - The Tumor Control Probability and Cancer 

Stem Cells 

Fipke 129 

Fipke 124 

Fipke 138 

Fipke 121 

Allan, Kara - A Model of the Spread of MRSA in a Hospital Fipke 140 

Sokolowsky, Benjmain - Achieving all Radio Numbers Fipke 129 


11:30 - 12:30 Keynote Speaker / Conférence plénière: Dominikus Noll 

- On Active and Passive Control 

Fip 204 

12:30 - 14:00 Lunch / Dîner Fipke Foyer 

14:00 - 15:00 

Lagacé, Jean - Proof of Brouwer Fixed Point Theorm, using 

Sperner’s Lemma 

Da Silva, Patrick - Factorial Function : Theorems and General- 

ization 

Chen, Li - A Taste of Homopy Groups and Classification of Prin- 

cipal Bundels Over S n 

Haris, Asad - Introduction to Markov Chain Monte Carlo and 

their Applications to ODE Models 

Huntemann, Svenja - On MDS Codes, the Main Conjecture, and 

the Partition Weight Enumerator 

Fipke 124 

Fipke 138 

Fipke 121 

Fipke 140 

Fipke 250 

Wanless, Michael - Knapsack-Based Cryptography Fipke 129 

15:00 - 15:30 Coffee Break / Pause café Fipke Foyer


15:30 - 16:30 Keynote Speaker / Conférence plénière: Gerda de Vries 

- The Language of Life: When Mathematics Speaks to Biology 

Fip 204 

17:30 Closing Banquet Opens / Banquet final Ramada Hotel 

18:30-18:45 Closing Remarks / Discours final Ramada Hotel 

18:45-19:45 Dinner / Souper Ramada Hotel 

19:45-20:00 Announcement of CUMC 2013 Host University / L’annonce de 

l’université d’accueil - Dessert 

Ramada Hotel 

20:00-1:00 DANCE DANCE! Ramada Hotel 

Sunday July 15, 2012 - Dimanche 15 juillet 


∀ t ∃x x ∈ Kelowna

2.3. ACTIVITIES / ACTIVITÉS 23 

2.3 Activities / Activités 

Thursday, July 12 - Jeudi le 12 juillet 

Ex Nihilo Winery Tour - Tour de cave à vin Ex Nihilo 

For those of you who have registered for the Ex Nihilo Winery Tour, your bus will be departing 

from the UBC Okanagan bus loop at 5pm. Ex Nihilo will be giving us a private tour of their wine 

making facilities, art gallery, and tasting room. This is a pre-registered event and we will not be 

taking registration for the event during the conference. 

Pour ceux d’entre vous qui se sont inscrits au tour de cave à vin Ex Nihilo, l’autobus partira 

de du terminus d’autobus de l’Université de Colombie-Britannique Okanagan à 17h. La compagnie 

Ex Nihilo nous fera faire un tour privé de ses installations de fabrication du vin, de sa galerie d’art 

et de sa salle de dégustation. Pour participer à cet événement, vous devez déjà être inscrit. Les 

inscriptions se seront pas possibles durant le congrés. 

Movie Night - Soirée de films 

For those of you who aren’t feeling adventurous today, we have booked the UBC Students’ Union 

Theatre for you to come, relax, and eat some popcorn (yes there will be popcorn!). The theatre is 

located in the University Centre (UNC) building. The show starts at 8pm. We will be showing “A 

Dangerous Method". 

Pour ceux qui n’ont pas trop le goût d’aventure aujourd’hui, nous avons réservé le UBC Students’ 

Union Theatre pour que vous puissiez relaxer en mangeant du pop-corn (oui, il y aura du pop-corn!). 

Ce cinéma se situe au University Centre (UNC). La projection débutera à 20h et le anglais film 

présenté sera “A Dangerous Method". 

Friday, July 13 - Vendredi le 13 juillet 

Women in Math and Science (WIMS) Dinner - Souper pour les Femmes en Maths 

et Sciences 

The CUMC 2012 is pleased to continue the tradition of offering a Women in Math and Science 

(WIMS) Dinner. The theme of this year dinner is “Breaking Down Barriers: Challenges Facing 

Female Mathematicians.” The evening will begin with a round table discussion, held in the Centre 

for Dialogue in the newly renovated Library at Okanagan College, where panelists from both in- 

dustry and academia will have the chance to share their experiences and discuss a range of topics.


Participants will have ample opportunity to join the conversation with their own questions as well. 

Afterwards, dinner with be served outside in the Courtyard in the beautiful Kelowna sunshine. 

During dinner, the participants and panelists will be encouraged to mingle and to continue their 

conversations. 

This year’s organizing committee has decided to make the dinner for women and woman- 

identified participants only. We thank you in advance for respecting our plans. 

Le CCÉM de 2012 est heureux de poursuivre la tradition d’offrir le souper Femmes en Maths 

et en Sciences. Cette année, le thème du souper est “Briser les barrières : Les Défis Rencontrés par 

les Femmes Mathématiciennes.” La soirée commencera par une discussion au “Centre for Dialogue” 

dans la partie renovée de la bibliothèque de l’Okanagan College. Les panlistes de l’industrie et de 

l’académie auront alors la chance de partager leurs expériences et d’aborder plusieurs sujets. Les 

participantes sont invitées à participer à la discussion en posant leurs propres questions. Ensuite, 

le souper sera servi dans la Cour sous le superbe soleil couchant de Kelowna. Pendant le souper, 

les participantes et panélistes seront encourages à se mélanger et poursuivre leurs conversations. 

Le comité organisateur de cette année a décidé de mettre en place ce souper pour les participantes 

seulement. Nous vous remercions à lvance de respecter nos plans. 

Scandia 

After our day at Okanagan College the 2012 organizing committee has arranged a fun evening 

at our local mini-golf and games centre, Scandia (www.scandiagolfandgames.com). There are retro- 

style arcade games, bumper cars, batting cages, and loads of mini-golf fun! Mini-golf starts around 

$10/game and arcade games at 1 token/game. Buses will be leaving Okanagan College at 6:30pm 

and 7:10pm to head to Scandia (enroute to UBC Okanagan) for an evening of fun. To get back to 

the university take the #97 - UBC Okanagan Express from the bus stop across the highway. 

Après la journée prévue à l’Okanagan College, le comité organisateur 2012 a prévu une soirée 

pour se relaxer au centre de jeux et de mini-golf local, Scandia (www.scandiagolfandgames.com). 

On y retrouve des jeux d’arcade de style rétro, des autos-tamponneuses, des cages de baseball et 

du mini-golf à volonté! Le prix du mini-golf commence à environ 10$ par partie et les jeux d’arcade 

coûtent un minimum d’un jeton par partie. Des autobus partiront de l’Okanagan College à 18h30 

et à 19h10 pour rejoindre Scandia, qui se trouve sur le chemin vers l’Université de Colombie- 

Britannique Okanagan, pour une soirée de plaisir. Pour retourner à lniversité, il suffit de prendre 

l’autobus #97 - UBC’s Okanagan Express à partir de lrrêt d’autobus de lutre côté de l’autoroute.

Abstracts / Résumés 

3.1 Keynote Abstracts / Résumés plénière 

Statistical Excursions in Sport 

Dr. Tim Swartz 

This talk explores some work that I have done and some topics that you may find interesting 

with respect to statistics in sport. Time permitting, some of the questions that I may cover include: 

When should you pull your goalie in hockey? 

Was the draft in the Indian Premier League (cricket) sensible? 

Do competitive Highland dancers perform in a fair order? 

Is there an age effect in minor hockey? 

When should you gamble in sports? 

An Invitation to Projection Methods 

Dr. Heinz H. Bauschke 

Feasibility problems, i.e., finding a solution satisfying certain constraints, are common in mathe- 

matics and the natural sciences. If the constraints have simple projectors (nearest point mappings), 

then one approach is to use these projectors in some algorithmic fashion to approximate a solution. 

In this talk, I will survey three methods (alternating projections, Dykstra, and Douglas- Rach- 

ford), and comment on recent advances and remaining challenges. 

25

26 CHAPTER 3. ABSTRACTS / RÉSUMÉS 

To All the Graphs I’ve Loved Before 

Dr. Donovan Hare 

What inspires me? Love inspires me. And me loves the graphs. 

I will show you some graphs I especially love and the problems they come from. Be warned: I’m 

not talking about graphing functions. No, I’m talking about the structure of love - relationships - 

and what can be dished about them. 

Sound crazy? It is. But then so is love. 

Finite Bases of Quasi-equations of Unary Algebras: How Few 

Rules Can We Get Away With 

Dr. Jennifer Hyndman 

The associative, distributive, commutative, negation and identity laws (equations) for the in- 

tegers are fundamental to our understanding of the integers. From childhood we “know" that 

everything follows from these laws. When we move to another algebraic structure a natural ques- 

tion is to ask what are the equations that hold and from which equations does everything else 

follow? 

When we allow for implications as well as equality we are considering expressions called quasi- 

equations. Sometimes when working with small algebraic structures with, say, 4 or 5 elements, our 

natural instinct that a few quasi-equations are sufficient to imply all quasi-equations is true. In 

other instances we require initely many quasi-equations to generate all quasi-equations. In this talk 

we see the variety of results that can arise in the seemingly simple situation of quasi-equations of 

small algebraic structures with only unary operations. 

Virologie in silico: cultiver des infections en ordinateur 

(In silico virology: growing infections in a computer) 

Dr. Catherine A.A. Beauchemin 

French talk with English slides 

L’expérimentation in vitro ou in vivo a longtemps éeté la seule et unique fa con d’étudier 

les infections virales. Cette méthode d’apprentissage est essentiellement fondée sur des postulats 

rarement contestés, du fait qu’il est diffcile detudier séparément une des composantes de ces systémes 

complexes sans en affecter une autre. Heureusement, les modéles mathématiques et informatiques

3.1. KEYNOTE ABSTRACTS / RÉSUMÉS PLÉNIÈRE 27 

nous permettent de déconstruire le système expérimental a d’identir ses composantes principales et 

de déterminer de quelle facon elles doivent être recombinées a de recréer la dynamique observée en 

laboratoire. 

Dans cet exposé, je présenterai des exemples de modèles mathématiques qui remettent en ques- 

tion la validité de certaines expériences d’infections in vitro et des exemples d’expériences in vitro 

qui nous forcent à revoir nos expressions mathématiques préférées. 

Experimentation in vitro and in vivo has traditionally been the only way to study viral infec- 

tions. This approach for deriving knowledge often relies on “common-sense" assumptions that go 

unchallenged due to the difficulties involved in controlling components of these complex systems 

without affecting others. Mathematical and computer models, however, make it possible to de- 

construct an experimental system into individual components and determine how the pieces come 

together to recreate the observed behaviour. 

In this talk, I will give examples of math models that challenge the validity of certain in vitro 

infection experiments, and of experiments that force us to consider more difficult math. 

On Active and Passive Control 

Dr. Dominikus Noll 

We will discuss passive control, also known as optimal control, and active control, also referred to 

as feedback control. We ask when these techniques are applied, what they have in common, in which 

sense they are complementary, and we discuss the mathematical techniques used to characterize 

and compute these control laws. 

The Language of Life: When Mathematics Speaks to Biology 

Dr. Gerda de Vries 

Mathematics often is described as the language of science, particularly suited to speak to prob- 

lems in physics, chemistry, engineering, and so on. Is mathematics also the language of life, suited 

to speak to problems in biology? Indeed, mathematics has a long and rich history in biology, and 

the reality is that today biology depends increasingly on data, algorithms, and models; mathemat- 

ics plays an extremely important role in biology. In this talk, I will highlight some particularly 

noteworthy historical contributions of mathematics in biology, dating back to the late 1600, make 

connections to contemporary research in mathematical biology, and discuss how this research im- 

pacts our lives.


3.2 Student Abstracts / Résumés des étudiants 

The student talks are arranged in alphabetical order by the speaker’s last name. The presentation 

will be in the language of the abstract, except if a note says otherwise. 

Les présentations étudiantes sont classées en ordre alphabétique selon le nom de famille de l’orateur. 

Elles seront présentées dans la même langue que le résumé, sauf si une note indique le contraire. 

An Irreducibility Criterion of A. Cohn 

Abdullah Al-Shaghay 

This talk explores an interesting irreducibility criterion, which is attributed to Arthur Cohn, 

for a particular subset of polynomials belonging to the ring Z[x]. I hope to discuss the significance 

of the theorem, examples of applying the theorem, and a conjecture which is closely related to the 

theorem. 

A Model Of The Spread of MRSA In A Hospital 

Kara Allan 

MRSA is a serious problem in most hospitals throughout the world. It is spread primarily by 

health care workers. This talk focuses on the model that I have been building since last summer to 

represent the spread of this disease. I use a stochastic SIS model with the population divided into 

patients and healthcare workers. The patients are further divided by rooms. I assume that there is 

no contact between patients, so that the healthcare worker is acting as the vector for transmission 

between patients. I will be studying the distribution of the time to extinction to understand the 

effects of intervention by healthcare workers. 

An overview of the some elements of spectral geometry 

Jean-François Arbour 

There are a lot of approaches to study a geometric object. Probably the most important idea 

for this has been the introduction of coordinates to view our geometric object as the solution of an 

equation of some sort, linking the geometry with algebra or calculus. In this talk, I will describe 

another approach: that of spectral geometry. Say you want to tell two random geometric objects 

apart. Well, a spectral geometer may be inclined to throw rocks at them and decide they are not 

the same if they don’t make the same noise! Another spectral geometer may put them on fire, put

3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 29 

one hand on each objects, and decide they are not the same if he burns his left hand first! Put it 

briefly, I will describe to you some of the finest technological tools we have to do geometry. 

Required background: First year undergraduate mathematics. 

Steiner Symmetriations: Convergence and Rate of Convergence 

Reza Asad 

Steiner symmetrization was invented in the 19 century as a tool for proving the isoperimetric 

inequality. The isoperimetric problem in the plane says that among all closed and simple curves 

of fixed length, the circle and only the circle encloses the most area. In the 1970, rearrangements 

like Steiner symmetrization gained new interest, because they proved to be useful for less obvious 

minimization problems in functional analysis. 

Steiner Symmetrization manipulates the shape of a body (or a function) without changing its 

size (norm). It is a classical fact that given an arbitrary convex body, there exists an appropriate 

sequence of Steiner symmetrizations that transforms it to a Euclidean ball. How well is full radial 

symmetrization approximated by sequences of such rearrangements? How fast do these sequences 

converge? These questions are subtle, because Steiner symmetrizations are neither linear, nor 

spatially localized and typically do not commute. 

In this talk, I will discuss works of a former U of T Master student Marc Fortier regarding 

Steiner symmetrizations applied to continuous functions with compact support. I will also state 

an open problem regarding the rate of convergence of such sequences of Steiner symmetrizations. 

Lastly, I will introduce ideas on how to approach the open problem. 

Required Background: Basic Analysis and Algebra 

Special Functions and Orthoganal Polynomials 

Micheal Baker 

I will give a lucid exposition of the theory of special functions and orthogonal polynomials 

(spherical harmonics, in particular, will be emphasized). The talk will be historically motivated by 

classical problems from mathematical physics. Some modest complex analysis will inevitably be a 

prerequisite.


Abelian and Additive Complexity: Analyzing Structure in Infinite 

Words 

Graham Banero 

Motivated by the problem of avoidability of abelian and additive squares, notions of the abelian 

and additive complexity of an infinite word w over a finite alphabet have been introduced as follows. 

The abelian complexity ρ ab (w, n) counts the maximum number of factors of w having length n, such 

that no two are permutations of each other; the additive complexity ρ Σ (w, n) counts the number 

of distinct sums of factors of w with length n. We give an overview of some main results on 

these relatively new concepts, paying attention in particular to the rich similarities and surprising 

differences between the two. 

Scaling Arguments on the Space of Connections 

Matthew Beckett 

The intent of this talk is to introduce Derrick scaling arguments. I will begin by giving give 

a (very) brief introduction to connections and deing the curvature form so that we are able to 

introduce the Yang-Mills action.We will work with the speci example of the Yang-Mills action, deed 

on the space of connections, to show how by rescaling the base space and then observing how this 

effects the action we can learn interesting information about critical points. Some prior knowledge 

of differential forms will be helpful, but not necessary. 

Principal Component Analysis and its Application to High Dimensional 

data Sets 

Nikolina Beg 

Data sets are getting bigger and bigger, with more and more variables. What can you do when 

your data set is so large you can analyze it efficiently? Principal Component Analysis (PCA) is a well 

known multivariate technique that can lead to effective dimension reduction, allowing statisticians 

to analyze their data set efficiently without losing information from the data. The concepts behind 

Principal Component Analysis will be introduced and its mathematical background explored, as 

well as how visualization techniques can be used to generate a better understanding of results. 

Then, the problem of dimension reduction on high dimensional data sets, specifically where p ≫ N, 

will be explored. Variations of PCA, such as Supervised Principal Components, will be investigated


in order to understand how a sub-sampling approach to a large problem can produce usable results 

and information. 

What is Understanding? 

Rene Bidart 

What does it mean when someone says they understand something? Is it the same for everyone 

or do people understand in different ways? why do some people excel when presented with rigorous 

proofs, which others simply could not grasp? this presentation will discuss the way in which people 

learn or understand “abstract” math, such as group theory, and more elementary topics in mathe- 

matics, such as basic arithmetic. It will consider the concept that understanding is visualization, 

along with the other possible ideas of what learning is. 

Calcul formel et programmation / Programming Computer Algebra 

Nicolas Bouchard 

Aujourd’hui, personne ne peut se passer d’ordinateurs, pas même les mathématiciens. Les 

logiciels, tels que Mathematica ou Maple, sont de plus en plus sophistiqués et permettent de faire 

des choses inouïes. Ils permettent de dériver des expressions complexes, ils peuvent jongler avec 

des groupes et même calculer des séries de Taylor. Mais comment? Ce n’est pas de la magie, c’est 

de la programmation! 

Nowadays, everybody uses a computer, even mathematicians. Softwares like Mathematica and 

Maple are getting more and more sophisticated and can do things quite unexpected. For instance, 

they can differentiate most expressions of any degree of complexity, they can use group theory, and 

even compute Taylor expansion. How? It is not magical, it is programming! 

Introduction to Stochastic Calculus 

Dylan Butson 

In the deterministic setting of real analysis one may dee the Riemann Stieltjes integral, which 

integrates one function with respect to another. In analogy with this, one can dee the integral of 

one stochastic process with respect to another, which is itself a new random process. Such integrals 

can be used to give meaning to stochastic di?erential equations and in many ways these ob jects


behave similarly to their deterministic counterparts. I introduce these concepts and motivate the 

key basic results of the sub ject. Topics include: Necessary background in the theory of stochastic 

processes; the Riemann-Stieltjes integral; the Ito integral; properties of the integral process; the Ito 

formula; examples throughout. 

Required Background: Only a knowledge of basic probability is assumed, but background in real 

analysis and stochastic processes will be useful. 

Cyclotomic Polynomials and Elementary Number Theory 

Manuel Candales 

The n-th cyclotomic polynomial Φn(x), (n a positive integer) is the monic polynomial Φn(x) = 

� (x−ζ) where ζ runs over all the n-th primitive roots of unity. It is an integer polynomial, and it is 

irreducible in Z[x]. The polynomial x n −1 factors in Z[x] in the following way: x n −1 = � 

d|n Φd(x). 

Historically, the cyclotomic polynomials (and cyclotomic number fields) have played a very 

important role in mathematics, because of their connection to fundamental problems, such as the 

constructibility of regular polygons and Fermat’s Last Theorem. 

In this talk we will discuss the applications of cyclotomic polynomials to solve problems in 

elementary number theory. We will introduce them and present some of their elementary properties. 

We will then use them to give elementary proofs of problems such as the infinitude of primes 

congruent to 1 modulo n (which is a special case of Dirichlet’s theorem on arithmetic progressions). 

Required Background: If you have some familiarity with elementary number theory and understood 

the first paragraph, then you are in good shape. 

DFAs, Automatic Numbers, and Transcendence 

Ian Charlesworth 

A common object within the theory of computing is the Deterministic Finite Automaton (DFA); 

roughly and informally, a DFA is like a computer with a finite (and often small) amount of memory 

available. These give rise to the definition of an automatic sequence as one which can be generated 

by a DFA, and an automatic real number in base-b as one whose base-b expansion is automatic. 

After introducing these concepts more rigorously, we will demonstrate a recent result of Boris 

Adamczewski and Yann Bugeaud from 2007: that any automatic number is either rational or 

transcendental.


Required background: Prior exposure to automatic numbers or sequences is not expected; ex- 

perience with DFAs will add to the talk, but the talk should still be accessible without it and they 

will be covered briefly at the start of the talk. 

Temperley Lieb Algebras 

Philippe Charron 

What happens when you take a vector space and embed it with some kind of vector multipli- 

cation? You get an algebra, which is a well-studied algebraeic object (no pun intended). I will 

introduce the Temperley-Lieb algebras, a family of algebras that were introduced to modelize cer- 

tain phase transitions and ice phenomenons in physics. Also, despite being ugly looking they admit 

a very natural visual presentation, which I will investigate in greater detail. 

A Taste of Homopy Groups and Classifications of Principal 

Bundels over S n 

Li Chen 

It seems so that mathematicians pursued after their agenda of pure abstractions while the 

physicists had less interest in the mathematical generalizations. The great divorce of mathematics 

and physics might have just occurred after their first rendez-vous in ancient Babylon. But when 

Einstein made his theory of general relativity, it seems that physics and mathematics came together 

once more as laws of nature are written by strokes of differential geometry. More than that, but 

the story that we are going to tell is one that is even more profound. It is what physicists call 

gauge fields. In this short talk, however, we will only venture to speak of the two basic concepts: 

homotopy groups and principal bundles. In particular, we will classify principal bundles over S n . If 

time permits, we will introduce connections on principal bundle, Yang-Mill functional, and matter 

fields. 

Finite State Automata and an Intrusion Detection System 

Kimberly Crosbie 

An Intrusion Detection System (IDS) is used to help protect computer networks from attacks 

and intrusions. One specific type of IDS is called signature-based network IDS. This kind of IDS 

monitors network traffic in search of malicious activity as specified in attack descriptions (referred to


as signatures). It has been discovered that several of these signatures can be triggered by the same 

set of packets, a situation which has been referred to as overlapping signatures. It has been shown 

that attacks on networks can occur by exploiting overlapping signatures. After a brief introduction 

to basic finite state automata theory, this talk will look at overlapping signatures in a commonly 

used IDS called Snort. By using set theory and finite state automata theory we will see how it is 

possible to quantify this overlapping signature problem. 

Predicting the Spatial Distribution of an Orchard Insect 

Pest 

Garrett Culos 

Codling moth is a pest which has plagued agriculturalists for the better part of the last century. 

Attempts in controlling this pest were successful until early 2000’s when of some mysterious reason 

the wild population began to increase. In an attempt to better understand this invasive pest a model 

was used to predict the percent of codling moths at arbitrary distance from there release point. 

This model is a deterministic diffusion-based partial differential equation which allows switching 

between two different movement modes. We used the experimental data to validate this model. 

Using the negative log-likelihood function and a recursive cubical division of parameter space to fit 

the data we obtained some extraordinary insight into the codling moth behaviour. 

Factorial Function : Theorems and Generalization 

Patrick Da Silva 

As it stands today, mathematicians in general know very few things of the factorial function 

outsidethe fact that it appears in the denominator of the terms in the Taylor expansion of an 

analytic function, the binomial coefficients and counting interpretations. In his paper, Manjul 

Bhargava wrote a paper which is generalizing the factorial function and exploring not-so-well- 

known theorems involving the factorial function. We will see that his generalization of the factorial 

function is quite natural from a number-theoretic point of view, and many questions arise from his 

paper. I will try to explain the theorems and the reasons behind the deitions of Manjul Bhargava. 

His paper can be found online by typing “ManjulBhargava Factorial” on Google.


Exploiting Known Structures to Approximated Normal Cones 

Chad Davis 

The normal cone to a constraint set plays a key role in optimization theory. We consider the 

question of how to approximate the normal cone to a set under the assumption that the set is 

provided through an oracle function or collection of oracle functions, but contains some exploitable 

structure. We provide a new simplex gradient based approximation technique that works for sets 

of the form 

S = {x � � gi(x) ≤ 0, i = 1, . . . , N} 

where each gi : R n → R is unknown and provided by an oracle. We further present novel results 

showing that, under a non-degeneracy condition, approximating normal cones to intersections of sets 

is possible by taking sums of approximations. Finally, we provide numerical results that exemplify 

the accuracy of the simplex gradient approximation when it is applicable, and the failure of this 

technique when a linear independence constraint qualification is not met. 

Connexions et calcul rigourex 

Andréa Deschênes 

Le calcul des solutions d’équations différentielles représente souvent un défi pour les scientifiques. 

En effet, les méthodes permettant de trouver ces solutions analytiquement s’appliquent rarement. 

Mais que faire lorsque la théorie ne nous permet pas d’aller plus loin? On doit alors mélanger les 

mathématiques numériques à l’analyse! Dans cet exposé, nous montrerons comment utiliser le calcul 

rigoureux pour trouver une connexion, un type particulier de solution d’une équation différentielle 

ordinaire. Pour ce faire, nous introduirons la notion de connexions homoclines et hétéroclines. Puis, 

les grandes étapes d’une méthode de calcul rigoureux seront présentées. Cette méthode permet de 

prouver, grâce à l’ordinateur et à l’analyse, l’existence d’une vraie connexion dans un voisinage 

autour de celle trouvée de manière numérique. Posséder quelques connaissances de base sur les 

équations différentielles représentera un atout pour comprendre cette présentation. 

The Tumor Control Probability and Cancer Stem Cells 

Andrew Dhawan 

This talk will provide an introduction to the mathematics underlying the tumor control prob- 

ability (TCP), as well as the relevant cancer biology, as they are used within the planning and 

modeling of radiotherapeutic treatments for cancer. The TCP is a formalism derived to compare


various treatment regimens of radiation therapy, and gives the probability that a prescribed dose of 

radiation eradicates, or controls, a tumor. The focus of this talk will be the development of a novel 

TCP model to account for the presence of cancer stem cells - a critically important subpopulation 

of cells found within the tumor mass. Such cancer stem cells are thought to drive the proliferation 

of the tumor, as they possess an unlimited replicative potential. Moreover, by analyzing tumor 

control through the control of stem cells, this talk will cover how this formulation of the TCP can 

be used in practice as a measurable quantity, as opposed to a theoretical one, via the results of 

immunohistochemical assays. 

Galois Theory and the Insolvability of the Quintic 

Annamaria Dosseva 

Methods for solving some quadratic equations were known since Babylonian times, around 300 

B.C., though the quadratic formula as we know it today was not discovered until around the ninth 

century, by the Persian mathematician al-Khowârizmî. The solution is outlined in his Algebra using 

the Greek method of geometry – our modern complete the square method. Over the next several 

hundred years, other mathematicians searched for a cubic formula that could be used to solve cubic 

equations, similar to the quadratic formula for quadratic equations. The solutions to the cubic and 

quartic were found during the 1500s through a combined effort of mathematicians at the Italian 

Mathematical School at Bologna. 

For nearly 300 years after that, algebraists searched for a general equation of the fifth degree. 

Paolo Ruffini (1765-1822) first proved that there is no general solution; Niels Henrik Abel (1802- 

1829) proved it as well, using a more rigorous argument than Ruffini’s; finally, Évariste Galois 

(1811-1832) showed the precise conditions for when a quintic – and, in general, for when an alge- 

braic equation of any degree – could be expressed as a finite number of additions, subtractions, 

multiplications, divisions, and a finite extraction of roots. 

Before discussing the problem, we will briefly review some of the language and theory of Abstract 

Algebra, namely the theories of Groups, Rings, Fields, Vector Spaces, and some Galois Theory. 

However, “Galois Theory is like garlic in that there is no such thing as a little of it. One must make 

a substantial study of it to appreciate the reasoning" (Carl B. Boyer). 

Required Background: A previous exposure to Groups, Rings, Fields and Vector Spaces will be 

useful, although not necessary as they will be covered briefly.


Rate of Convergence of Random Polarizations 

Anne Dranovski 

His talk will give a description of simple rearrangements known as polarizations, or two-point 

symmetrizations, and an outline of a convergence problem which is the topic of a summer research 

project. 

Required Background: basic analysis and probability. 

Supplemental Learning: A New Way to Learn Mathematics! 

Jodie Foster 

Supplemental Learning (SL) is a peer lead program that targets historically difficult courses in 

order to help students improve their understanding of course material. In particular, it allows stu- 

dents to get together to discuss important concepts and develop strategies for studying the subject. 

Supplemental Learning Leaders are exceptional students who have taken the course previously and 

are prepared to share what they have learned over the years when studying that particular topic. 

SL applies techniques such as: turning questions, student teaching, and the Boardwork Model. SL 

is not limited to only mathematics, but also in an assortment of subjects such as applied science, 

art history, biology, chemistry, geography, human kinetics, physics and psychology. Who are we if 

not professional learners? It is up to us to lend ourselves and our undergraduate experiences to 

those just beginning to immerse themselves into the world of mathematics. 

Stabilization Time for a Type of Evolution on Binary Strings 

Jacob Funk 

We consider a type of evolution on {0, 1} n inspired by an elementary question about a line 

of soldiers, each of whom are attempting to find the right direction to face. Mathematically, we 

consider a string consisting of n binary bits, and engage in a process of simultaneously replacing 

every instance of “01” in this string with “10”. By doing so, new instances of “01” are created 

(for instance “0101” ↦→ “1010”, with a new instance of “01” appearing in the middle). Thus the 

same operation as above can be performed on the new string that was obtained, and so on. It is 

elementary to show that this process of recursively creating new strings stabilizes after at most n−1 

iterations, with the final string being of the form 11 · · · 1100 · · · 00. The time of stabilization for a 

random string in {0, 1} n is thus a random variable with values in {0, 1, . . . , n − 1}. My talk will


present results describing the asymptotic behaviour of this random variable for n → ∞. The tools 

used in the arguments are a natural interpretation of strings in {0, 1} n as Young diagrams, and a 

connection with the known distribution for the maximal height of a Brownian path on [0, 1]. This 

is a joint project with Mihai Nica and Michael Noyes, and is part of my current NSERC USRA 

term in the Pure Mathematics Department at Waterloo. 

Introduction to Modular Forms 

Mathilde Gerbelli-Gauthier 

The aim of this talk will be to give an intuitive introduction to a class of highly symmetric 

complex functions: Modular Forms. In order to do this, we will study the group of automorphisms 

of the complex upper half-plane and its discrete subgroups. This will allow us to dee modular 

forms, to derive some of their properties, and to get a glimpse of their relation to number theory. 

Drawings included! 

Required background: complex numbers, familiarity with groups. 

Introduction à l’Homologie Singuliére 

Kevin Gervais 

En topologie, il peut être très difficile de déterminer si deux espaces donnés sont différents l’un 

de l’autre. Une technique très efficace qui nous permet de diffé rencier les espaces topologiques 

consiste à associer aux espaces une structure algébrique. Les groupes d’homologie en sont un bel 

exemple. Non seulement permettent-ils de différencier (à homotopie près) les espaces topologiques, 

ils permettent ègalement d’offrir des preuves très élégantes pour de nombreux théorèmes, tels que : 

le théorème du point e de Brouwer, le théorème de Jordan et l’invariance de la dimension. Je propose 

donc de vous introduire aux groupes d’homologie et de présenter certaines de leurs propriétés. 

Analysis around Fractals 

Jonathan Godin - Engish talk with French slides 

How can we create a fractal? This presentation will introduce some useful analysis tools such 

as metric spaces, Hausdorff distance, and iterated function system (IFS) so that we can create 

some interesting sets in R 2 . Basic real analysis knowledge such as convergence of a sequence and 

continuity are necessary for a better understanding of the concepts.


Introduction to Markov Chain Monte Carlo and their application 

to ODE models 

Asad Haris 

Markov Chain Monte Carlo (MCMC) methods have long been used to simulate samples from 

a given target distribution. In the past few decades numerous MCMC algorithms have been de- 

veloped and improvements have been made to the existing algorithms. This talk will begin with 

a short introduction to Bayesian statistics, the theory of Markov Chains and a brief description of 

certain basic MCMC algorithms. In Bayesian Statistics, on many occasions, we obtain only partial 

knowledge about the distribution of a random variable. The first part of the talk will focus on 

such circumstances and hence lead to the discussion on the motivation of sampling techniques and 

MCMC methods. 

In the second part of the talk I will demonstrate the use of Bayesian computational tools to 

estimate parameters in an Ordinary Differential Equation (ODE) Model. ODE models can are used 

in many sciences to model numerous systems and in many cases have many parameters associated 

with the model. Due to multiple parameters, the usual sampling techniques prove to be inefficient 

and hence advanced MCMC methods are used. This talk will review and compare some of the 

recent advancements to MCMC algorithms. The model under consideration will be the Fitz-Hugh 

Nagumo Model which aptly demonstrates the usual computational problems associated with such 

problems of parameter estimation. 

Finally, I will discuss my current research and possible ideas for future research. This talk will 

assume only a basic knowledge of probability and is open to all interested in applied computational 

statistics. 

Exponential Model of the Eiffel Tower 

Josh Holt, Richard Hudson, Bryan Zintel 

Equations modeling the shape of the Eiffel Tower are investigated. We have developed an 

exponential model based on the equilibrium of moments and embodied wind load on the tower. 

The result yields an exponential profile of the tower. We analyze the actual Eiffel Tower Profile 

to show that this profile may be closely approximated by two piecewise exponential curves with 

different growth rates.


Qualitative Analysis of Chemical Reaction Networks 

Joseph Horan 

We are often interested in investigating non-linear dynamical systems, which are nigh impossible 

to solve explicitly for the most part; however, there exist numerous methods of qualitative analysis 

we can use to determine if there are equilibrium points or periodic orbits, on which subspaces 

do solutions reside, and how stable limit points/sets are, amongst other things. One particular 

class of non-linear systems which is interesting is that of chemical reaction networks; this is the 

subject of my summer research. Here, I briefly review the notation for such systems, and in 

a survey style, present a pseudo-graph-theoretic approach developed by Vol’pert, as well as the 

row/column diagonal dominance Lyapunov method developed by many, all illustrated by the same 

simple example, that of the enzyme model. A method for finding conservation relations, by Schuster 

and Höfer, is also discussed. I posit questions for the future, due to the open nature of the field. 

The convergence criterias of the bayesian Monte Carlo Simulation 

on the quantification of the number of fluorophores in 

a cell 

Chieh-Ting(Jimmy) Hsu 

Photobleaching of fluorophores in a cell e.g. Green Fluorescent Protein(GFP) is a stochastic 

process, which is similar to radioactive decay. Though it leads to an exponential decay on average, 

the fluctuations away from the average exponential decay are not white noise, so traditional least- 

squares fits of the decay are not appropriate. Since the fluctuations are due to the photobleach 

events, we can use them to quantify the number of fluorophores in a cell. To extract the fluctua- 

tions we need the average decay, however real photobleach data of bacteria expressing GFP shows 

stochastic exponential decay in each cell, though with a variety of timescales that prevent us from 

simply averaging different cells together. 

What if we have only a single cell? I will present our Monte Carlo Maximum Likelihood with 

Bayesian statistics approach that allows us to extract information (or “fit”) a photobleach decay 

for an individual cell and find out the number of initial GFP that we have while focussing on the 

convergence criterias needed during the simulation in order to explore enough parameter space to 

reach convergence. 

Note: Even though the abstract involves biology terminology, the talk only involves mathematics 

and statistics with abosolutely no biology background required.


Cooking Howard’s Curry With The Agda Programming Language 

Sean Hunt 

This talk will be an introduction to the Curry-Howard correspondance between proofs in formal 

logic systems and type checking in programming languages. This remarkable observation allows 

for veriation of proofs by way of checking that a computer program compiles. This is exploited by 

computer systems such as Coq and Agda to allow for formal veriation of proofs. 

The talk will include a brief explanation of the correspondance, but the main focus will be on 

taking advantage of the correspondance with the Agda programming language in order to make 

non-trivial proof. The limitations of this environment, both in terms of the limitations of what can 

be proved, as well as requirements for human interaction. The speaker hopes to, time permitting, be 

able demonstrate a proof of an interesting but relatively simple elementary theorem of mathematics. 

Required Background: none 

Derivative Free Optimization: An Investigation of Algorithms 

on Sample Functions 

Spencer Hunt 

From the dawn of time, it has been known that extremely powerful data can be found in the 

derivatives of any function one wishes to optimize. Many "standard" definitions of local minima, 

given by first-order necessary conditions, are in fact, for continuously differentiable functions, that 

the first-order derivatives are indeed zero. In a fantastical world, all functions would have easily 

attainable derivatives. But this is the Real World–seven strangers, picked to live in a house–and 

not all functions provide reliable derivatives. Is is because of this, that the branch of derivative-free 

optimization was born. I will be discussing three basic derivative-free optimization techniques and 

applying them to a number of sample functions. These functions are made to test the robustness of 

the algorithms. As well, they will highlight some of the problems that many mathematicians face 

in derivative-free optimization. Please join me in our exploration into derivative-free optimization, 

a world of mystery and wonder.


On MDS Codes, the Main Conjecture, and the Partition Weight 

Enumerator 

Svenja Huntemann 

Maximum Distance Separable (MDS) codes are those error-correction codes that have the largest 

possible minimum distance, which means that they can correct more errors than any other type of 

code. MDS codes have many applications in the industry and every-day life. 

One important area of research concerning this type of codes is finding an upper bound on 

the length n of the codewords given the alphabet size q and the dimension k. This long-standing 

problem is also important for combinatorial and experimental designs and in finite geometry. 

For linear MDS codes there has recently been a great advance towards solving this problem and 

proving the main conjecture to be true. The main conjecture states that the upper bound on n is 

q + 1, except for k = 3 or k = q − 1 and q even, where it is q + 2. 

For general, not necessarily linear, MDS codes very little is known about the upper bound. A 

summary of known upper bounds with an emphasis on bounds related to the main conjecture will 

be presented. 

A new technique for proving these upper bounds in the general case uses the partition weight enu- 

merator (PWE). The PWE for linear MDS codes has been introduced by El-Khamy and McEliece 

(2005), and their proof can be easily adjusted for general MDS codes. Several examples deriving 

upper bounds using the PWE together with other combinatorial techniques will be given. 

An Individual Based Model for Bear Movement 

Andrea Hyde 

The International Bear Association lists 6 of the 8 bear species world wide as endangered or 

threatened. Neither the American Black Bear or the Brown Bear are currently listed. However, 

with the expansion of tourism, and industry into the back country, the increased rate of human bear 

interactions may change that. This project aims to understand the effect that different Human- 

Bear Management strategies have on the movement patterns and rates of human bear interactions 

in Communities. I will present a novel individual-based model for bear movement in which the 

displacement of a bear from one habitat patch to another follows a probability function. It is not 

known exactly what this function should depend upon, and so our mathematical approach is helping 

to elucidate the motivating factors for bear movement, their relative importance, and the dispersal 

patterns that result. 

Preliminary investigations show that including the location of food sources and of Human-Bear 

Interactions (HBI) is sufficient to create realistic movement patterns for an individual bear.


An Introduction to Topology 

Neal Jackett 

Topology is the study of how properties of the domain and range affect the behaviour of a 

continuous mapping. We will explore the concept of topological spaces and subspaces and the 

continuity inherent in them. We will also discuss connectivity and compactness of topological 

spaces and look at familiar examples. 

A Simple Proof of the Jordan Curve Theorem 

Ifaz Kabir 

The Jordan Curve Theorem states an obvious, but hard to prove fact: that a simple closed curve 

divides the plane into two components, one bounded and one unbounded. In this talk I will attempt 

to give a simple proof of the Jordan Curve Theorem assuming some easy to prove ‘hammers’ such 

as the Brouwer Fixed Point Theorem. 

Representations and Duality with a View towards Number Theory 

Jamie Klassen 

I will provide a quick, flashy and results-oriented approach to representation theory (focusing 

on finite groups and providing analogies to linear algebraic groups when necessary) and discuss 

some elementary results concerning Kronecker coefficients and Schur-Weyl duality as well as some 

indications of their broader consequences in the realm of automorphic forms and modern number 

theory. Students will need some familiarity with the concepts of linear algebra and basic abstract 

algebra. As an example, you should understand what GLn means and what Sd the symmetric 

group is, ideally as well as the significance of such topics as number fields and Galois theory. 

Flows, Branching Numbers, and Percolation on Trees 

Jason Klusowski 

Let T be a locally finite tree and fix p ∈ [0, 1]. For each vertex v of T , randomly declare v to be 

open with probability p. Otherwise v will be closed with probability 1 − p. Make the choice of the 

state of each vertex independent of the state of every other vertex of T . A path P in T is open if 

all the vertices of P are open in T .


A natural question to ask is if there exists a critical probability in which such open paths exist 

in T with positive probability, and if so, how it might relate to Galton-Watson branching processes 

conditioned on survival? I will answer this question by introducing the concepts of a flow and a 

branching number along with some of their elementary properties and a couple of examples. 

An Introduction to Machine Learning for Text Classification 

Michelle Kovesi 

How can a computer be programmed to classify inputs into various categories? The answer, 

often, is to use machine learning. Machine learning is a branch of artificial intelligence that is 

concerned with making computers evolve in response to input. This talk will give a basic introduc- 

tion to the topic of machine learning for text classification. It will include information on how to 

prepare text documents for classification, as well as how the classification algorithms actually work. 

As an example, we will look at a basic classification algorithm called the Perceptron. Finally, I will 

present a new multi-lingual classifier that I implemented last summer. 

Required Knowledge: none 

Proof of Brouwer Fixed Point Theorem, using Sperner’s 

Lemma 

Jean Lagacé 

Brouwer Fixed Point Theorem states that any continuous mapping from a compact convex 

subset of an Euclidean space into itself has a ed point, i.e. a point such that f(x) = x. While this 

theorem is considered to be one of the key theorems concerning the topology of Euclidian spaces, 

it has applications in many mathematical lds, ranging from differential equations to game theory. 

As such, a variety of proofs arise with arguments coming from a wide range of lds. Here, a graph 

theory result, Sperner Lemma, will be used to prove that the Brouwer Fixed Point Theorem is true 

for any simplex in R n , and, since the ed point property is conserved by homeomorphisms, true for 

any compact convex subset of R n .


Brain, Dynamical Systems and Fun! 

Jean-Sébastien Lévesque 

Dans plusieurs régisons du cerveau, les neurones s’organisent en petits groupes capables de 

produire des oscillations. Ces oscillateurs neuronaux interagissent entre eux par de faibles connex- 

ions et peuvent précenter divers phénomènes de synchronisation. Dans cet exposé, il sera ques- 

tion d’oscillateurs faiblement couplés et principalement de différentes dynamiques (comportement 

péiodique, quasi-péiodique, synchronisation) observables sur un tore, l’espace de phase naturelle- 

ment associé à un système de deux oscillateurs couplés. 

Required Background: At least one eye, to see great pictures and cool videos! 

The Roots of Flow and Chromatic Polynomials 

Richard Leyland 

Using graph flows one can model many different phenomena such as electricity or networks. So 

it is important to know if a graph has a k-flow. The flow polynomial ΦG(x) tells us the number of 

such flows. It turns out the flow polynomial is related to the chromatic polynomial of the planar 

dual χG∗(x), which tells us the number of k colorings. In a paper by Sokal, he shows that the roots 

of chromatic polynomials are dense in the complex plane. I will discuss this result and what we 

results we hope to obtain with flow polynomials, along with some conjecture regarding the roots of 

flow polynomials. 

Combinatorial Designs and Block-Intersections Graphs 

Robert Luther 

A combinatorial design D is a pair (V, B) where V is a set of distinct points and B is a set of 

subsets of V called blocks. 

A pairwise balanced design P BD(v, K, λ) is a design D = (V, B) where v = |V | and each pair of 

points of V occurs in exactly λ blocks of B. In addition, the cardinality of each block of B must be 

an element of K. If K should consist of a single element, say K = {k}, then the design is called a 

balanced incomplete block design BIBD(v, k, λ). In addition to the constant block size in a BIBD, 

there is a fifth parameter r called the replication number which is the number of times any one 

point of V occurs in the blocks of B.


The block-intersection graph of a design D = (V, B) is the graph GD having the block set B as 

its vertex set and such that two vertices B1 and B2 are adjacent if and only if (B1 ∩ B2) �= ∅. 

A cycle in a graph G is a closed path in G such that no vertex is repeated more than once. 

A cycle that contains every vertex in a graph is called a Hamilton cycle and if a graph G has a 

Hamilton cycle, then G is called Hamiltonian. A graph G is called pancyclic if G has a cycle of 

every possible length, from a 3-cycle to a Hamilton cycle. 

We discuss some known results about cycles in block-intersection graphs of BIBDs and of 

P BDs as well as some open questions regarding cycles in these block-intersection graphs. 

Using Symmetry Groups to Solve Partial Differential Equations 

Keenan Lyon 

Many of the useful properties of symmetry groups on partial differential equations (PDEs) arise 

from the fact that they are Lie groups, which are differentiable manifolds endowed with a group 

structure. The smooth manifold part of the Lie group allows one to continuously vary the elements 

in the Lie group. The idea of using group theory to solve ODEs first originated at the turn of the 

century by Sophus Lie. Although he did not finish his work, the applications of his Lie groups and 

Lie algebras are ever present in many fields of math, and the technique of using symmetry groups 

to find PDE solutions is still a matter of much research. 

PDEs model systems that depend on several variables. For example, the schrodinger equation is 

a PDE where the solutions depend on both the position of a particle and the time of the system; it 

is the fundamental of non-relativistic quantum mechanics. The heat equation is another example, 

and it models the distribution of heat over time given some initial condition, and it can also be used 

to model particle diffusion. These two examples show the various applications that PDEs have in 

describing natural processes. 

The spirit of finding symmetry groups of PDEs is that one solution, via some group element of 

the symmetry group, can be transformed into another solution. Since the groups are Lie groups, this 

implies a family of infinite solutions which can be created from just one solution. The motivation 

behind this talk is to outline the basic algorithm first created by Lie to find solutions. On the 

way to applying the algorithm, and extensive look into Lie groups, vector fields, group actions and 

topology will be aided by examples.


Fundamental Theorem of Calculus for Lebesgue Integration 

Richard Mack 

The Fundamental Theorem of Calculus is one of the core results in analysis. However, in its 

standard form taught in beginning calculus/analysis courses, it applies only when the function has 

continuous derivatives, which is a very small class of functions. In my talk, I will be discussing a 

generalization of the Fundamental Theorem of Calculus to the Lebesgue integral, and the proof in 

the context of measure theory, based on Lebesgue-Radon-Nicodym theorem and absolute continuity. 

This talk will be aimed toward an audience with some exposure to measure theory. 

Introduction aux méthodes de Schwarz 

Dominique Maheux 

Plusieurs méthodes de résolution matricelle sont à notre disposition. D’une part, on connaît la 

méthode de la matrice inverse ou la décomposition LU, qui sont des méthodes directes. D’autre 

part, il existe aussi certaines méthodes itératives qui permettent d’approximer la solution désirée. 

Toutefois, les méthodes directes sont souvent trop coûteuses et les méthodes itératives ne sont pas 

toujours très robustes. Nous allons proposer un compromis entre ces deux types de méthodes, soit 

la décomposition de domaine. Nous présenterons quelques méthodes de Schwarz en expliquant les 

avantages et les inconvénients de ces méthodes. 

Il s’agit d’une présentation très simple qui ne nécessite que quelques notions de base i.e. savoir 

ce qu’est une équation et une dérivée! 

Structure of Neural Networks 

Isaiah Mandryk 

Artificial neural networks are computational models inspired by the way neurons pass informa- 

tion via synapses in the brain. They are effective for modelling complex nonlinear relationships 

between an input and output set of data vectors where there is little or no a priori information 

about the relationships, and are also very helpful for discovering patterns in data. The connec- 

tivity between nodes in the network is often represented by a graph, with neurons as nodes and 

synapses as edges. The structure of this graph can have enormous implications on the performance 

of the neural network. This talk focuses on the different types of structures typically used in neural 

network implementations and the effects the different architectures have on the network. These 

include differences in the capability of the network to generalize the learned information to apply


to new data, the number of mathematical operations (and thus the amount of time) required to 

train the network, and the capacity for the network to approximate arbitrary functions. 

Introduction to Additive Frieze Patterns 

Jean-François Marceau 

Additive Frieze Patterns are pure combinatorial objects that were developed by G.C. Shephard 

in 1976. Even if they are now 36 years old, just few mathematicians studied them so they are not 

well known. In this talk, I will present the results I got from my research on the subject during 

summer 2011 (see arXiv 1205.5213). 

Weyl’s Theorem 

Joanie Martineau 

Weyl’s theorem is the first interesting result found in spectral geometry. This theorem gives 

us an asymptotic expression for the number of eigenvalues of the Laplacian operator for bounded 

domains in Euclidean space. This talk will introduce the basic concepts of spectral geometry and 

prove intuitively Weyl’s theorem. 

Dirichlet Series and Arithmetic Functions 

Kevin Mather 

We will discuss basic detions and convergence of Dirichlet Series, construction of Dirichlet Series 

by Arithmetic Functions, factorization of Dirichlet Series, and the similarities of Dirichlet Series to 

power series 

The Story of Srinivasa Ramanujan 

Arthur Mehta 

The talk will be split into segments. The first segment will consist of a brief telling of the one 

of the most romantic stories in the history of mathematics: the story of Srinivasa Ramanujan. 

Ramanujan was a self-taught Indian mathematician who was born into poverty. After years of 

obscurity his talent was finally recognized by G.H Hardy, a prominent mathematician at Trinity


College, Cambridge. The discovery of Ramanjuan eventually resulted with him traveling to England 

to work alongside Hardy. This led to one of the most productive mathematical partnerships of the 

20th century, and resulted in works contributing to a wide variety of areas, including Number theory, 

Analytic Combinatorics, Infinite Fractions and Infinite Series. This segment will be followed by a 

segment devoted to examining a select set of works completed by Ramanujan. These works will 

include a look at Ramanujan work on Highly Composite Numbers: his contribution to determining 

the number of partitions of a given number. Lastly we will examine a host of intriguing identities, 

infinite series and infinite fractions produced by Ramanujan. 

Required background: none 

From Differential Equations to Diphtheria: the Mathematics 

of Infectiouse Disease Spread 

Irena Papst - English talk with Bilingual slides 

In recent years, mathematical modeling has become an important tool in epidemiology. Math- 

ematicians are able to create models of infectious disease spread which can be used predict the 

outcome of an outbreak in different populations, as well as the effectiveness of various control 

strategies, all without risking the public’s safety. This tool enables public health agencies to make 

well-founded decisions in high-risk situations. 

In this talk, we will introduce the concept of mathematical modeling and discuss what makes 

a good model. We will focus on the application to epidemiology and consider one of the simplest 

epidemiological models, the SIR model, in order to draw important conclusions from it. However, 

models are not perfect; they must be set up, adjusted, and interpreted carefully, while bring mindful 

of observed data. We will analyze the simple SIR model in the context of childhood diseases such 

as measles, mumps, and rubella, and adjust it accordingly to make other important conclusions 

about the dynamics of these infectious diseases. 

Recommended background: First year calculus, some experience with ordinary differential equa- 

tions.


Diophantine Approximations 

Hongyoul (Mike) Park 

The field of Diophantine approximations is the study of the approximation of real numbers by 

rational numbers. 

First, we need to make sure that the problem of rational approximation is well formulated. Let 

α be some real number which we would like to approximate by rational numbers. We know that 

rational numbers Q form a dense set on the real line R; this means that we can always find a 

rational number arbitrarily close to α. Moreover, for any ε > 0, there are infinitely many rationals 

a/b ∈ Q satisfying |α − a/b| < ε. Thus, we need to adjust the problem. 

One possible approach is to make ε depend on denominators of rational approximations. Specif- 

ically, let ε(b) = 1/b k where k is some positive integer. Are there rational numbers which satisfy 

|α − a/b| < ε(b)? How many rationals (finitely many or infinitely many) satisfy this inequality? 

As it turns out, the answers to these questions depend not only on the value of k, but also on the 

intrinsic properties of the number we seek to approximate! For instance, there are famous theorems 

by Liouville and Roth which assert that algebraic numbers cannot be approximated “too well" by 

rationals. 

In my talk, I will discuss how algebraic numbers behave with respect to Diophantine approxi- 

mations. I will construct examples of numbers which have very good rational approximations and, 

therefore, cannot be algebraic. I will also explain how to find good rational approximations using 

the theory of continued fractions. 

A Brief History of Women in Mathematics 

Crystal Parras 

This presentation was inspired by my first encounter reading about a female mathematician, 

Sophie Germain. The lengths at which she went to study mathematics against her parents’ wishes 

fascinated me. This lead me to explore further stories of other women in mathematics: the contri- 

bution they made, the people they interacted with, the lives they lived. This presentation will give 

a brief overview of the lives of some female mathematicians, whose stories have caught my eye. 

Probability and Measure 

Laurent Pelletier 

In this talk, we will try to motivate and introduce the concepts of measure theory by proba- 

bilistic means. The concept of a measure is fundamental in probability theory. On the other hand,


probabilities give an interesting meaning to the usual objects of measure theory. Subsets become 

events, σ-algebras talk about independence.... 

Required Background: You don’t need to know about measure theory, a basic probability course 

will be enough. 

Investigating Orthogonal Latin Squares Using Universal Algebra 

David Peterson 

Latin squares are simple mathematical objects that are familiar to anyone who has solved a 

Sudoku puzzle – a special type of Latin square. Basically a Latin square is a square matrix of 

entries from some set S such that every element of S occurs in every column and every row. We 

will be investigating pairs of orthogonal Latin squares; that is, a pair of Latin squares A, B with 

entries from some set S such that for every (a, b) ∈ S 2 there is a unique pair of row i and column 

j such that (aij, bij) = (a, b). We will explore these structures by converting them to algebraic 

structures, thereby allowing us to take advantage algebraic techniques (as well as providing a good 

excuse to do some neat algebra). In particular, we will refute a conjecture by Euler stating that it 

is impossible to find a pair of orthogonal Latin squares if |S| ≡ 2 (mod 4). 

Required Background: Some familiarity with basic abstract algebra, especially group theory, 

is helpful but not strictly necessary as this talk aims to be reasonably self contained. Everyone is 

welcome and should get something out of the talk. 

Math and Art: the math behind the beauty 

Tara Petrie 

Many people are skeptical when they hear that math and art are interwoven throughout history 

and that in some universities you can get a math degree through the faculty of arts; but the truth 

is that although they seem like very different subjects, math and art have influenced and grown 

from each other since their creation. My talk focuses on the influence of mathematics in art and 

architecture, particularly concerning the golden ratio and certain geometric shapes and patterns. I 

was very fortunate to spend two weeks of May studying in Italy; the vast art and architecture in 

that area inspired me to learn more about the math behind the beauty. 

Because the connections between math and art are so numerous, I have decided to concentrate 

mainly on Ancient times and the Renaissance as well as some modern mathematical art, with my


presentation set up as a timeline. I start by explaining the Golden Ratio, geometric shapes designed 

according to the Golden Ratio, and its influence on the Great Pyramids and the Parthenon. I 

then discuss ancient artist and mathematician Polykleitos and his Canon. Next I move to the 

Renaissance, focusing on the development of perspective including Piero della Francesca logical art 

in his De Prospectiva Pingendi as well as the various mathematical influences within Leonardo da 

Vinci work. Lastly, I give a quick discussion on more modern mathematical art from M.C. Escher, 

John Robinson, and various others. 

I believe this is a good topic because no matter at which level an undergraduate student stands, 

he or she will be able to understand and find value in this discussion. With particular emphasis on 

geometry and perspective and using specific examples of art and architecture throughout history, 

I hope to ignite in my audience the same fascination I have with two interconnected subjects that 

are commonly viewed as polar opposites. 

On the Existence of Double Arithmetic Progressions 

Andrew Poelstra 

Van der Waerden’s Theorem states that for any number of colors r, and any length k, every 

r-coloring of the natural numbers must contain a monochromatic k-term arithmetic progression (a 

sequence x1, x2, . . . , xk with constant gap between consecutive entries.) 

We extend this idea to double k-term arithmetic progressions: sets xi1 , xi2 , . . . , xik which have 

constant gap between consecutive entries, and constant gap between consecutive indices. 

We ask whether every r-coloring of the natural numbers must contain a k-term arithmetic 

progression, present computational evidence to suggest that the answer is (in general) no, and show 

that this question is equivalent to one about infinite words on finite alphabets. 

A Topological Proof of the Infinitude of Primes 

Alex Provost 

It is well-known that there is an infinite number of primes; Euclid offered the first known proof 

of that statement circa 300 BC. 

In this talk I will give a beautiful proof of the infinitude of primes using elementary notions of 

point-set topology. This modern proof was discovered in 1955 by mathematician Furstenberg. No 

anterior knowledge of topology is assumed; the basic concepts (topological space, closed and open 

sets, base) will be explained along the way.


VC Dimension and Density: Connections between Computational 

Learning Theory and Model Theory 

Nigel Pynn-Coates 

In this talk we will introduce the notions of Vapnik-Chervonenkis dimension and density de- 

veloped in computational learning theory. These notions are important because they determine 

whether a concept is uniformly learnable, a key question in computational learning theory. Along 

the way, we will also consider some standard mathematical examples to help clarify these ideas. 

Model theory is a branch of mathematical logic seemingly unconnected to computational learning 

theory. In fact, there is an interesting connection and we will see how a model-theoretic perspective 

leads to new results about VC theory. In particular, it is used to prove uniform bounds on VC 

density in different structures. Finally, we will consider a theorem from computational learning 

theory (translated into probability theory) and discuss how we can use the theorem to guess at the 

VC dimension or density of families of sets. 

Recommended background knowledge: some elementary logic would be helpful (e.g. formulas, 

realisations) but is not required to understand most of the talk. 

Causal Inference and Bayesian Propensity Score Adjustment 

Methods 

Léo Raymond-Belzile 

Often times, in the context of policy analysis or medical research, one is interested in establishing 

causal relationship between variables, for example the effect of legislation on individual’s behaviour 

or the impact of a drug on survival. The purpose of the talk is to introduce the Rubin Causal 

Model framework along with the various challenges faced in the area of causal inference. I will 

introduce some basic statistical notions, as well as confounding, propensity score adjustment (PSA) 

and ways to adjust for uncertainty in the context of missing data problem. The incapacity of the 

PSA method to incorporate uncertainty arising from the evaluation of the propensity score model 

justifies some recent literature on Bayesian PSA which will be discussed. A first course in statistics 

is assumed.


Critical Issues in Statistical and Biological Interpretation 

Jeremy Recoskie 

Within the field of medicine, there is a constant written dialogue through various medical 

journals, papers, and reports. Professionals within the academic disciplines of medicine, health, 

biology, statistics, and mathematics are primary contributors to these texts. Due to the complexity 

involving many disciplines, authors, and researchers, there is a clear need for a common language 

of dissemination so that the results of these texts may be more easily interpreted across multiple 

disciplines. 

In a recent survey of the 2009 H1N1 pandemic literature, there were several instances where 

semantic and statistical misinterpretation or miscommunication arose. These examples could be of 

use to interdisciplinary groups or researchers in the field of medicine. 

The focus of this talk is on the mathematical and statistical issues realized through the literature 

reviewed, however some semantic issues will also be mentioned. Included will be examples of 

how improper use of hypothesis testing, density fitting, citations and terminology contribute to a 

decreased quality of research texts. Discussion of all aspects is key to the goal of a more precise 

understanding of the many texts that comprise medical research. 

Simplicial k-Complexes and Packings: Touching (k + 1)-tuples of 

Congruent Balls in 3-space 

Samuel Reid 

By generalizing the problem in combinatorial geometry of determining the maximum number 

of touching unit balls in a packing of n unit balls, we define a class of problems captured by the ∆- 

function, ∆k d (n), which determines the maximum number of touching (k+1)-tuples of unit d-balls in 

a packing of n unit balls in Ed . The case of k = 1 was studied by Heiko Harborth in E2 (1974) and 

Károly Bezdek in E 3 (2010), where Harborth proved the precise result of ∆ 1 2(n) = ⌊3n − √ 12n − 3⌋ 

and Bezdek gave an upper bound of ∆ 1 3(n) < 6n−0.695n 2/3 , provided n ≥ 2. By applying Bezdek’s 

upper bound on ∆ 1 3(n) to the case of pairwise touching 4-tuples (quadruplets) of spheres in E 3 , 

and using a simple combinatorial argument, we prove an initial bound of ∆ 3 3(n) < 4n − 0.463n 2/3 . 

To improve this upper bound independent of the bounds for k = 1, we construct an approach 

to finding upper bounds on ∆k d (n), where k ≥ 2, by observing that ∆k d (n) equivalently describes 

the maximum cardinality of a simplicial k-complex K in Ed determined by an n-element point set 

in E d , where the minimum distance between points is of twice the radius of the unit d-ball. By 

proving two key lemmas, that (1) at most four tetrahedra can share an edge in K, and (2) at most 

twelve tetrahedra can share a vertex in K, we prove that ∆ 3 3(n) ≤ 12n/4 = 3n. We propose a


research program to determine the behaviour of the ∆-function in non-Euclidean geometries, such 

as spherical and hyperbolic geometry, as well as in higher dimensions. 

Lost in Intervention: Conditioning of Spectral Collocation 

Methods 

Sarah Reimer 

Spectral collocation methods are used to solve boundary value problems for ordinary differen- 

tial equations with narrow boundary layers. The numerical results are very accurate, despite the 

sometimes severe ill-conditioning of the system matrices arising. Equations with zero boundary 

conditions do not amplify perturbations, but equations with nonzero boundary conditions do. By 

solving an equation with inhomogeneous boundary conditions in two steps we maintain accuracy 

and increase the robustness of our method. 

Pattern Subgroups of GLn(F) 

Larissa Richards 

This talk assumes knowledge from an Introductory Course in Abstract Algebra/Group Theory 

and is built from a chapter of G.D. James’ Representations of General Linear Groups with the 

help of Professor Fernando Szchetman. The theory of representation of the symmetric groups 

is extremely elegant and can be used in several ways to find representations of other groups. In 

addition, their theory has applications in fields such as quantum mechanics and polynomial identity 

algebras. There is a close connection between the representations of the symmetric groups over a 

field F and the representations of GLn(F) over the same field. The finite general linear group is 

associated to a finite subset of a real vector space with certain combinatorial properties known 

as its root system. The classification of GLn(F) reduces to the classification of root systems and 

the structure of any of these groups can be obtained from properties of its root system. We will 

introduce the pattern (root) subgroups of GLn(F) and prove an easy result which is of fundamental 

importance in the representations of GLn(F). This will lead us to two interesting open problems.


Introduction to Estimation 

William Ruth 

Making predictions is one of the most fascinating problems in statistics. It allows for everything 

from engineering buildings to deciding the risk of heart attacks in cardiac patients. I this talk, I 

will introduce a popular framework for predictions and 2 models that have been proposed to handle 

it. 

The framework being discussed is called regression, in which a response variable (dependent 

variable) is predicted based on knowledge of some set of predictor variables (independent variables). 

The first model, known as linear regression, s the more well known of the two models and will share 

the first 1/3 of the talk with setting up the framework. This model consists of expressing the 

response variable as a linear combinations of the predictor variables and choosing the ’best’ such 

linear combination. The second model is called a regression tree and is only usually taught i 

graduate courses on data mining. This model will also receive about 1/3 of the talk and consists 

of partitioning the data then estimating each part ion separately. The final third of the talk will 

be split between a few topics related to the two models. This will included a discussion of how to 

evaluate a model, a comparison of the strengths and weaknesses of each of the models discussed, 

and a brief introduction to a few procedures that extend the basic regression tree structure. 

This will be an elementary presentation that assumes almost no background in statistics (if you 

know what a mean is then you’re good). As such, it will be more of an overview of a few areas 

than in in-depth analysis of one topic. In conclusion, this talk is a good opportunity to get an 

introduction to a fascinating and widely applicable area in statistics. 

As Easy as A, B, C 

Philip Ryan 

This talk introduces the ABC Conjecture in number theory, also known as the Oesterle-Masser 

Conjecture. If A, B, and C are natural numbers with no common factors, with A + B = C, 

when is it possible that C is larger than the product of the prime factors of ABC (that is, the 

largest square-free factor of ABC)? The conjecture claims "very rarely," and if true, it provides an 

incredibly powerful tool which can be applied to a deep well of number theory, including Fermat’s 

Last Theorem and the Erdos-Mullin-Walsh conjecture on triplets of powerful numbers, as well as 

a host of other results and conjectures. I will explain the conjecture in full and work through an 

example of its use. 

Required background: Basic arithmetic


Continuous Model Theory and von Neumann Algebras 

Nigel Sequeira 

In my talk, I will introduce the topic of my summer research project: von Neumann algebras 

and some modern model theoretic approaches to their study. Basics ideas from operator theory 

and, more specifically, from the theory of von Neumann algebras, will be discussed. In particular, 

we will look at the operator-theoretic methods and constructions necessary to discuss aspects of 

the classification of type II factors; emphasis will be put on the type III factors, or tracial von Neu- 

mann algebras with trivial centres. Additionally, I will talk about some applications of continuous 

first-order logic in the context of von Neumann algebras, which will allow us to examine some of 

the current research and results from the intersection of operator theory and model theory. 

Assumed knowledge: A good course in linear algebra, basic logic and analysis. Basic topology 

and more analysis is a plus, but not required. The required operator theory and model theory will 

be introduced as needed. 

Euclid’s Elements and Pythagoras’ Theorem 

Nicolas Simard 

This talk is divided into two parts. In the first part, I will present some important facts (that 

all mathematicians should know) about Euclid’s elements and Pythagoras’ theorem. I will then 

explain the first book in more details, particularly the first rigorous proof of the Pythagorean 

theorem that Euclid elaborated. In the second part, it will be your turn to talk! Indeed, those who 

wish may share their knowledge by presenting, in than 150 seconds, a proof of the Pythagorean 

theorem. Try to find the most elegant, simple, and original proof! But do not forget, I’ve got the 

one from Euclid! 

Representations of Harmonic Donuts 

Michael Snarski 

What do a donut, real matrices with determinant one and the integers have to do with each 

other? What is the relationship between triangles, three letters, a 6-vertex directed graph – and 

how can one "represent" this relationship? What do R/Z, 2×2 orthogonal matrices and eigenspaces 

of the Laplacian ∆f = d2 f 

dx 2 have in common?


As undergraduates, there are many fascinating connections between different fields of mathemat- 

ics we have yet to explore. This will be an example-based, picture-motivated chalk-talk which hopes 

to give a glimpse of some big ideas in math and give you an idea of what certain “buzz” words mean. 

Prerequisites include linear algebra (eigenstuff) and a first course in abstract algebra (familiarity 

with group structure). 

Achieving All Radio Numbers 

Benjmain(Ben) Sokolowsky 

For a connected graph G, a radio labelling is a function c : V (G) → Z + such that for every pair 

of vertices (u, v) in V (G), the radio condition is satisfied: 

distance(u, v) + | c(u) − c(v) | ≥ diameter(G) + 1. 

The span of a radio labelling c is the largest integer in the image of c. The radio number of a graph 

G is the smallest integer M such that span(c) = M for some radio labelling c. It is known that a 

graph of n vertices has a radio number of at least n and at most (n−1)2 

2 

+ r, where r is determined 

by the parity of n. This presentation discusses three-parameter graphs known as Sok graphs. We 

show that for all but two integers between the known minimum and maximum, there exists a Sok 

graph whose radio number is that integer. The results of this work entirely settle the question of 

what the possible radio numbers are for graphs of order n. In addition, we present a generalization 

of distance maximization, a well known technique for determining lower bounds of radio numbers, 

and show that the bounds are sharp for an infinite family of graphs. 

Intuition and Probability 

Colin Street 

Intuition can be a powerful tool for day-to-day application, but it can also lead us to draw 

false conclusions. This talk will examine how some common cognitive biases conflict with statistics 

both in regular application and in some notable cases, and show how some simple applications of 

probability can help. 

Required Background : none ’


Lie Group Methods for Moving Mesh Algorithms 

Simon Szatmari - English talk with French slides 

In the realm of numerical computation, the aim is to approximate with the help of a computer 

the solutions of a PDE with as much speed and accuracy as possible. However, some PDEs still 

resist our attemps to solve them numerically. 

Consequently, the use of Lie Groups has recently penetrated the domain of what is called 

Geometric Integration. More precisely, we can transform Iterative Methods into Canonical Iterative 

Methods that respect the subjacent Lie Group structures of the PDE. 

My talk will focus on the following three aspects. To begin with, I will give an intuitive expla- 

nation of what Lie Groups are and how they work. It will be followed by a brief introduction to 

what Moving Mesh Methods are, how they work and why they are necessary. When combining the 

two ideas, I will demonstrate how Lie Group Methods come about, what enhencements they bring 

and what new avenues of research are currently explored. 

Modeling Techniques of Genetic Information Flow: Past and 

Future 

Caleb Tarzwell 

This presentation will discuss the results and findings of an NSERC-USRA funded survey con- 

ducted in the summer of 2012 at the University of Northern British Columbia of modeling techniques 

in molecular biology. Numerous mathematical models have been proposed since Francis Crick’s pro- 

posal of the Central Dogma of Molecular Biology. The Central Dogma has since been disproven 

but is still commonly used to describe the nonlinear and multidirectional flow of information be- 

tween the nucleus and the ribosome. An introduction to the Central Dogma and the challenging 

problems which arise will be provided for listeners without a background in Molecular Biology. 

Three promising models will be presented: finite state machines, matrix algebra with connections 

to group theory, and hidden markov models. These mathematical and probabilistic models attempt 

to describe the flow of genetic information within a cell. The most common application has been 

describing the transition from DNA to RNA to protein. The three models will be presented with 

their relative merits and weaknesses and situations in which they are best employed. After the 

introduction of these, a dynamic model describing the complete flow of information within the cell 

will be presented consisting of various components of each of the three models. Future steps for this 

NSERC funded survey will then be discussed. The most intriguing of these are obtaining better pre- 

diction mechanisms for RNA and protein structure. The presentation will conclude with discussing 

the need for researchers with an interdisciplinary background to bridge the differences between


methodologies between mathematicians and molecular biologists to speed further developments in 

molecular biology. 

Introducing Uniformly Distributed Sequences 

Arman Tavakoli 

I will motivate and introduce the idea of a uniformly distributed sequence using a Monte Carlo 

simulation. After a few example sequences, I will discuss a celebrated theorem by Hermann Weyl 

called Weyl’s criterion. The rest of the talk will be about different kinds of uniformly distributed 

sequences. 

Parallel Parking with Lie Algebras 

Selim Tawfik 

Using the language of Lie algebras, we will see that an idealized driver is always able to parallel 

park provided there is enough room for their vehicle to fit. We will start by quickly defining 

manifolds, vector fields, Lie groups, Lie algebras and Lie brackets, and stating important results 

connecting these notions. 

Required Background: Basic differential geometry would help, but not strictly necessary. 

Domination Polynomials of Graphs and Their Roots 

Julia Tufts 

We say that a set of vertices, S, is dominating if every vertex of the graph is in S or adjacent to 

a vertex in S. The domination polynomial of a graph G is the generating function of the number 

of dominating sets of each size in G. 

The domination polynomial is a relatively new polynomial, and as is the case with other graph 

polynomials, the roots are of great interest. This talk will discuss the nature and location of the 

roots of domination polynomials. We find that the roots for certain families of graphs often create 

distinct patterns that we are able to analyze, and we also obtain a surprising result for the set of 

all domination roots.


Opportunities in Mathematical Biology 

Rebecca Tyson 

Mathematical Biology is an exciting discipline at the interface of mathematics and biology. Many 

biological questions are intractable when approached with biological techniques alone, but can be 

solved with the power of mathematical tools. The breadth and variety of the field is enormous, 

from differential equation modelling of forest fires or the inner workings of cells to interacting 

particle systems models of recolonization or evolutionary processes. We begin the session with an 

introduction to the field given by three speakers from the University of British Columbia, Okanagan 

and Vancouver campuses, and the University of Alberta. We then discuss graduate programs in 

mathematical biology in Canada, and future careers. 

Knapsack-Based Crytography 

Michael Wanless 

At the heart of every public-key cryptosystem is a computationally difficult problem that pro- 

vides security for the system. Thus, problems that are known to be hard hold a lot of interest for 

cryptologists and number theorists in general. An example of such a problem is the knapsack or 

subset-sum problem, which is proven to be NP-complete. This talk will provide an introduction to 

the ideas behind classical public-key cryptosystems based upon the knapsack problem, using the 

Merkle-Hellman cryptosystem as a case-study. We will examine how the security of these cryp- 

tosystems is tied to finding short vectors in lattices, and thus how the LLL algorithm can be used 

to break many such systems. 

Prerequisites: An understanding of modular arithmetic is nearly esse 

The Shortest Introduction to Semidefinite Programming 

Gwen Yun Weng 

Semidefinite programs often capture the mathematical essence of problems of various structures. 

Therefore, semidefinite programming is used in theoretical and practical explorations of a wide range 

of problems. This talk will cover the very basics of semidefinite programming and demonstrate its 

application to a typical eigenvalue optimization problem. 

Required background: Basic Linear Algebra. Exposure to Linear Programming will be helpful.


Game Theory and Evolution 

Toban Wiebe 

Game theory is essential for understanding evolution. Organisms are in competition for survival; 

as such, there is a strategic aspect to natural selection. This talk will provide an introduction to 

game theory and its use in modelling evolution. Classical game theory examines equilibria produced 

by rational players using optimal strategies. Evolutionary game theory adds an extra stability 

condition for equilibrium: that no small mutant population can invade a population in equilibrium. 

The model can be further extended to analyze the dynamics of evolution. No prior knowledge of 

game theory is required. 

A Winning Strategy 

Wu, Steven 

Billions are poured into a gambling industry annually that is designed for the house edge to 

rake in profits. A New York Times bestseller written by Edward O. Thorp resulted from the 

phenomenon discovered that flipped the odds of one casino game, Blackjack, in favour to the 

player. After a brief overview on the rules of how to play, features that distinguish it as capable of 

a positive expectation for the player, I will detail the pertinent mathematics that explain how each 

unique rule, from doubling down to the option of taking insurance, affects the expectation of the 

game. After describing what constitutes “Basic Strategy”, I will show how Thorp manipulated the 

probabilities using card counting to produce a winning strategy that swept the nation through use 

of examples of certain game scenarios. 

Required background: None, previous knowledge of the rules of Blackjack and expected value will 

help to follow along. 

Statistical Refinement of Astrophysical Numerical Simulations 

Miayan Yeremi 

The process of star formation is the fundamental agent at determining how an isolated galaxy 

like our own evolves over the course of the universe. Many physical processes contribute to star 

formation (gravitation, magnetism, chemistry, radiation, and fluid dynamics). However, it is not 

understood exactly how these effects shape the process of star formation. Physical observations


from radio telescopes provide some insight into the process of star formation but alone do not 

provide the necessary information to understand exactly how the physical process evolves. Properly 

designing and experiment to study star formation is complicated by many factors. A single run 

of the computer model can take upwards of five thousand hours, in addition some of the input 

variables evolve during the code runs meaning that the inputs of the computer code are observed 

with error. Lastly, comparing code runs to physical observations is complicated by things, first we 

must compare three dimensional data cubes and secondly simple euclidean distances between these 

cubes is not correct measure of similarity between these two objects. In this talk we will discuss 

some recent work on the design and analysis of complex experiments to study star formation. The 

ultimate gal of this study is to provide a physically meaningful description of how stars evolve. 

How Topologically Inclined Thieves Split Their Spoils 

Jonathan Zung 

More often than one might expect, a pair of thieves is confronted with the following problem. 

Having stolen a necklace with k different types of jewels, they wish to cut up the necklace so that 

each of the two receives the same number of jewels of each type. In 1985, thieves the world over 

rejoiced when Douglas West and Charles Goldberg showed us how to split such necklaces equitably 

with at most k cuts. Amazingly, their approach uses a topological argument. In this talk, I will 

present a slick proof of this result due to Alon and West.

General Information / 

Informations générales 

4.1 Internet connections on campus / Connexions Internet 

sur les campus 

UBC’s Okanagan campus 

Connect to the network “ubcvisitor”. You will be directed to a website where you must enter in 

your email to log on. 

Se connecter au réseau “ubcvisitor”. Vous serez dirigés vers une page qui vous demande un email 

pour s’inscrire. 

Okanagan College 

Okanagan College does not have a visitor network that we can use. The school has provided us 

with a few usernames and passwords if you require internet for your presentation. These can be 

used for presentations only. The volunteer in your presentation room can issue you a username and 

password to use if you need it. 

L’Okanagan College n’a pas de réseau pour les visiteurs. L’école nous a donné quelques noms et 

mots de passe pour ceux qui auront besoin d’une connexion internet pour leur présentation. Ils ne 

sont disponibles que pour les présentations. Le bénévole de votre salle de présentation s’occupera 

de vous les fournir. 

64

4.2. GETTING TO/FROM OKANAGAN COLLEGE AND THE CLOSING BANQUET 65 

4.2 Getting to/from Okanagan College and the closing ban- 

quet 

There will be a day of talks held at Okanagan College (OC), 1000 KLO Rd, on Friday, July 13th. 

All talks will be held in Building E, The Centre for Learning. 

The closing banquet, will be held at the Ramada Hotel, 2170 Harvey Ave (Hwy 97N). 

Buses have been arranged to transport people to/from UBC’s Okanagan campus to OC and 

to/from the Ramada Hotel for the closing banquet. If you need a ride to OC or the closing 

banquet, please sign up for the buses so that we can ensure everyone at the conference who needs 

a ride gets one. If you do not sign up for a bus, or you miss your bus, we cannot guarantee that 

you will be able to get on the next one. 

Public transport does go to each of the venues. To get to OC from UBC take the #8 - Okanagan 

College and get off at Okanagan College. To get to the Ramada Hotel from UBC take the #97 - 

Express, get off at Cooper Rd near Orchard Park Mall, and walk approximately 450m east to the 

Ramada. 

If you are driving to any of the venues, there is parking available. OC Facilities has told us that 

parking is free of charge on the day we are there. Parking is not free at UBC’s Okanagan campus; 

you must purchase a parking pass from one of the ticket dispensers. If you decide to drive to the 

closing banquet, please decide on a designated driver beforehand. Please do not drink and drive! 

You are also more than welcome to leave your vehicle overnight at the Ramada and take the bus 

back to the university, or one of the volunteers can arrange a cab for you. 

Aller et revenir de Okanagan college et du banquet final 

Une journée de présentation sera tenue au Okanagan College (OC), 1000 KLO Rd, le vendredi 

13 juillet. Toutes les présentations seront donnes au Pavillon E, The Centre for Learning. 

Le banquet final se tiendra au Ramada Hotel, 2170 Harvey Ave (Hwy 97N). 

Un transport en autobus a été prévu pour l’aller et le retour entre le campus de UBC Okanagan 

et l’Okanagan College ainsi que pour le banquet final au Ramada Hotel. S vous avez besoin d’un 

transport vers l’Okanagan College pour le banquet final, veuillez vous inscrire afin de s’assurer que 

tous ceux qui auront besoin d’un transport en auront un. Si vous ne vous inscrivez pas ou que vous 

manquez votre autobus, nous ne pouvons pas vous assurer que vous pourrez prendre le prochain 

transport. 

Le réseau d’autobus dessert l’Okanagan College. Pour se rendre à ’C de UBC, prenez l’autobus 

#8 - Okanagan College et sortez à l’arrêt Okanagan College. Pour aller au Ramada Hotel à partir 

de UBC, prenez l’autobus #97 - Express, sotez à Cooper Rd près de Orchard Park Mall et marchez

66 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES 

environ 450m vers l’est. 

Si vous vous rendez en automobile à l’un de ces deux endroits, des stationnements seront 

disponibles. Les stationnements de l’OC seront gratuits lors de notre passage. Le stationnement 

n’est pas gratuit sur le campus de UBC; vous devez acheter un ticket de stationnement à l’une des 

bornes. Si vous décider de conduire pour vous rendre au banquet, décidez d’un conducteur désigné. 

S’il vous plait, ne conduisez pas après avoir bu! Vous pouvez aussi laisser votre véhicule sur les 

lieux du banquet final et prendre l’autobus. Il est aussi possible d’appeler un taxi. 

Friday, July 13 - Vendredi 13 juillet 

• Sign-up for buses to Okanagan College will happen Thursday, July 12th during coffee breaks 

and lunch. People presenting on Friday need to be on the 7:45am bus to pre-load presentations. 

• Sign-up for buses to UBC Okanagan will happen Friday, July 13th during coffee breaks and 

lunch. 

• L’inscription pour les autobus vers Okanagan College aura lieu le jeudi 12 juillet durant 

les pauses-caf et l’heure du midi. Les participants qui donnent une présentation le vendredi 

doivent prendre l’autobus de 7h45 afin de transférer leur diaporama. 

• L’inscription pour les autobus vers UBC Okanagan aura lieu le vendredi 13 juillet durant les 

pauses-ca’e et l’heure du midi. 

Leave/Départ Arriving / Arrivée Bus/ Autobus 

7:45 8:05 to/vers Okanagan College (2 buses) 


18:30 18:50 to/vers UBC Okanagan, via Scandia 


19:50 20:10 to/vers UBC Okanagan 

20:30 20:50 to/vers UBC Okanagan (WIMS participants only)

4.3. KELOWNA TRANSIT INFORMATION / LE TRANSPORT EN COMMUN Á KELOWNA67 

Saturday, July 14th - Samedi 14 juillet 

• Sign-up for buses to the Ramada Hotel will happen Saturday, July 14th during coffee breaks 

and lunch. 

• There is no sign-up required for buses leaving the Ramada Hotel. 

• L’inscription pour les autobus vers le Ramada Hotel aura lieu le samedi 14 juillet durant les 

pauses-ca’e et l’heure du midi. 

• Il n’y a pas d’inscription préalable pour les autobus du Ramada Hotel vers UBC Okanagan. 

Leave/Départ Arriving / Arrivée Bus/ Autobus 





0:30 0:40 to/vers UBC Okanagan 

1:00 1:10 to/vers UBC Okanagan (WIMS participants only) 

4.3 Kelowna transit information / Le transport en commun 

á Kelowna 

The main bus that travels between UBC Okanagan campus and downtown is the 97 - Express. The 

bus that runs from UBC to Okanagan College to downtown is the 8 - Okanagan College. Fare for 

public transport is $2.25 and drivers carry no change. 

You can view Kelowna transit schedules and maps at www.transitbc.com/regions/kel. 

L’autobus principal qui dessert le campus de l’Université ainsi que le centre-ville est le #97- 

Express. L’autobus qui fait le parcours du Okanagan College vers le centre-ville est le #8-Okanagan 

College. Le coût d’un aller est de 2,75$. Ayez l’argent exact puisque les conducteurs n’ont pas de 

monnaie. 

Vous pouvez trouver tous les trajets d’autobus et les horaire au www.transitbc.com/regions/kel.

68 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES

4.4. GREAT PLACES TO EAT IN KELOWNA / BONS ENDROITS OÙ MANGER À KELOWNA69 

4.4 Great places to eat in Kelowna / Bons endroits où manger 

à Kelowna 

Breakfast / Déjeuners 

The Jammery, 8038 Hwy 97 N, www.jammery.com ($) 

Bread Co., 363 Bernard Ave, thebreadcompany.ca ($) 

Bohemian Cafe, 524 Bernard Ave, www.bohemiancater.com ($$) 

Cafes / Cafés 

The Cannery, 1289 Ellis St ($) 

The Bean Scene, 274 Bernard Ave ($) 

Lunch / Dîners 

Bread Co., 363 Bernard Ave, thebreadcompany.ca ($) 

Mediterranean Market, 1570 Gordon Dr ($) 

Wood Fire Bakery, 2041 Harvey Ave ($$) 

Dinner / Soupers 

Pubs 

Fernando’s Taqueria, 279 Bernard Ave ($$) 

Twisted Tomato, 371 Bernard Ave, twistedtomatokitchen.com ($$) 

Poppadoms - Taste India!, 948 McCurdy Rd, www.poppadoms.ca ($$) 

DunnEnzie’s Pizza, 1559 Ellis St, www.dunnenzies.com ($$) 

Mon Thong Thai, 1876 Cooper Rd, www.monthong.ca ($$) 

RauDZ, 1560 Water St, www.raudz.com ($$$) 

Doc Willoughby’s Pub, 353 Bernard Avenue, www.docwilloughby.com ($$) 

O’ Flannigan’s Pub , 319 Queensway ($$) 

Rose’s Waterfront Pub, 1352 Water St, www.rosespub.com ($$) 

Turtle Bay Pub, 2850 Woodsdale Rd, Lake Country, www.turtlebaypub.com ($$) 

$ under 10 per entree / Moins de 10 $ 

$$ 10-15 per entree / Entre 10 $ et 15 $ 

$$$ 15-25 per entree / Entre 15$ et 25$


4.5 Fun things to do in Kelowna / Activités amusantes à 

Kelowna: 

Knox Mountain 

Located north of the downtown area, about a 25min walk or 5min drive north from Queensway 

Bus Loop, down Ellis St. Alternatively, you can bus there on the #2 - North End Shuttle 

and get off at Cambridge Ave˙and Ellis St. There are many walking trails on this mountain, 

short, long, steep, and gentle. You may find people mountain biking on the trails. There 

is a look out halfway up and another at the top, which you can also drive to if you have a 

vehicle. From here you can take in the beautiful views of Okanagan Lake and its surrounding 

mountains, stretching off into the horizon. Take good walking shoes and plenty of water! 

Cette montagne est située au nord de la région du centre-ville, à environ 25 minutes de marche 

ou 5 minutes de voiture au nord de Queensway Bus Loop, sur Ellis St. Vous pouvez aussi 

vous y rendre en autobus en prenant la #2 - North End Shuttle et en descendant au coin 

Cambridge Ave. et Ellis St. On retrouve sur cette montagne plusieurs pistes de randonnée, 

qu’elles soient courtes ou longues, abruptes ou douces. Certains font même de la bicyclette 

sur ces pistes. Il y a un point de vue à mi-chemin et un autre, au sommet de la montagne, 

où vous pouvez vous rendre en voiture. De là, vous pourrez admirer l’Okanagan Lake et les 

montagnes avoisinantes qui s’étendent jusqu’á l’horizon. N’oubliez pas de bons souliers de 

marche et beaucoup d’eau! 

City Park and Beach 

Located a hop, step, and a skip away from downtown Kelowna, at the end of Bernard Ave 

and parallel to Abbott St, City Park and its beach, on Okanagan Lake, is a great place to 

people watch, go swimming, and relax in the sun. Take your swimsuit and towel! 

Situés tout près du centre-ville de Kelowna, au bout de Bernard Ave. et paralèle Abbott 

St., City Park et sa plage sur le bord de l’Okanagan Lake sont un bel endroit où aller pour 

admirer la vue, se baigner et relaxer un peu au soleil. Apportez avec vous votre maillot de 

bain et votre serviette! 

Beyond the Crux 

This climbing gym is located at #2 - 1414 Hunter Court. There are walls are fixed with auto 

belays so that you can climb away to your heart’s content! A day pass is $15 and it is open

4.5. FUN THINGS TO DO IN KELOWNA / ACTIVITÉS AMUSANTES À KELOWNA: 71 

Monday to Friday, 4 - 10pm and Saturday, 11am - 5pm. For more information check out 

www.beyondthecrux.info. 

Ce gymnase d’escalade est situ au # 2 - 1414 Hunter Court. Il y a des murs équipés d’auto- 

assureurs pour que vous puissiez grimpez autant que vous le voulez. La passe de journée coûte 

15$ et le centre est ouvert du lundi au vendredi de 16h à 22h ainsi que le samedi de 11h à 

17h. Pour plus d’information: www.beyondthecrux.info. 

Rusty’s Steakhouse 

Don’t let the name fool you, this is a billiard hall. They have 10-12 tables for just food and 

have a full menu available that can be brought to the tables. The key bonus for this place 

is they have a lot of tables, and it’s very far from a ’dirty pool hall’ - very open space, not 

smoky, newly renovated, clientele are mostly students and middle aged men... Located at #1 

- 1525 Dilworth Dr. Checkout www.rustyssteakhouse.ca for more information. 

Ne laissez pas le nom vous tromper, il s’agit d’une salle de billard. Une dizaine de tables sont 

disponibles pour manger et un menu complet est fait pour être servi directement aux tables de 

billard. L’avantage de l’endroit est qu’il y a un grand nombre de tables et qu’il n’y a aucune 

comparaison à faire avec les bars de billard miteux -tràs ouvert, pas enfumé, nouvellement 

rénové, la clientèle est constituée en grande partie d’étudiants et de jeunes hommes. Situé au 

#1 - 1525 Dilworth Dr. Allez au www.rustyssteakhouse.ca pour plus d’informations. 

Walk the Mission Creek Greenway 

The Greenway is a 17km pathway that runs throughout Kelowna from Lakeshore Drive, near 

the lake at Truswell Rd, up to the Rutland and Black Mountain areas. It is a gentle walk and 

is used by many Kelownians for walking, running, biking, and horseback riding along Mission 

Creek. For more information check out www.greenway.kelowna.bc.ca. 

Le voie verte est une voie de 17 kilomètres de sentiers traversent Kelowna à partir de Lakeshore 

Drive, près du lac à la route Truswell Rd, jusqu’à Rutland et au secteur Black Mountain. C’est 

un trajet accessible utilisé par les habitants de Kelowna pour marcher, courir, faire du vélo 

et du cheval. Pour plus d’informations, visitez le www.greenway.kelowna.bc.ca. 

Walk along the waterfront 

A great place to go for a stroll is the path along the waterfront. It runs parallel to Water St, 

starting downtown at the corner of Bernard Ave and Abbott St, travelling north to Waterfront


Park. Here you’ll find a quiet beach to chill out on. If you continue to the very end you’ll 

come to a peaceful waterfowl sanctuary with a boardwalk running through it. 

L’endroit parfait pour prendre une marche est la rive du lac Okanagan. Les quais sont 

paralléles á Water St, partant au centre-ville au coin de Bernard Ave et Abbott St, jusqu’au 

nord á Waterfront Park. Á cet endroit, vous trouverez une jolie plage pour relaxer. Au bout 

de cette plage se trouve un endroit magnifique qui vaut le détour. 

4.6 CUMC 2013 Host Bids / Enchères pour accueillir le CCÉM 

2013 

The CUMC could not continue without its host school. We strongly encourage you to consider 

making a bid to host CUMC 2013 at your school. First you need to check with your home depart- 

ment to get approval for hosting. Once you get approval, inform one of the organizers that your 

school would like to put in a bid for CUMC 2013. 

On Friday, July 13th at 5:30pm, representatives from each university that wish to be considered 

as next year host university will give a brief presentation about their school and city. Ballots will 

be distributed following the presentations and will be collected at lunch on Saturday, July 14. Each 

participating university is given one vote, regardless of how many of its students are attending the 

conference. In a change from previous years, the winner will be decided using the Schulze Method, 

a modern and widely-used voting system that uses a preferential ballot. Rather than voting for 

a single option, each university’s ballot will allow the candidate host universities to be ranked in 

order of preference. The preferential ballots will then be input into a computer which uses the 

Schulze Method to determine the winner. We have chosen to use the Schulze Method because it 

is mathematically interesting, it is modern, it satisfies an extremely wide range of academic voting 

system criteria (Condorcet criterion, majority criterion, independence of clones, etc.), and it has 

been adopted by many reputable organizations such as the Wikimedia Foundation. The winning 

host university will be announced at the closing banquet. 

Enchères pour accueillir le CCÉM 2013 

Le CCÉM ne peut pas exister sans une université hôte pour l’accueillir. Nous vous invitons à 

penser à la possibilité de participer à l’enchère pour organiser l’évènement ln prochain. La première 

chose à faire serait de véfifier si le département de mathématiques de votre université est favorable 

à une telle candidature. Une fois lutorisation obtenue, informez un organisateur que votre école 

aimerait déposer sa candidature.

4.6. CUMC 2013 HOST BIDS / ENCHÈRES POUR ACCUEILLIR LE CCÉM 2013 73 

Le vendredi 13 juillet à 17:30, les représentants de chaque université participant à lnchère don- 

neront une brève présentation à propos de leur école et de leur ville. Les bulletins de vote seront 

distribués suite aux présentations et seront rammassés le midi suivant. Chaque université partici- 

pante a droit à un vote, peu importe le nombre d’étudiants présents. Contrairement aux dernières 

années, le gagnant sera déterminé par la méthode de Schulze, une méthode de vote moderne et 

largement utilisée qui utilise un vote à classement. Au lieu de voter pour une seule université, 

chaque bulletin permettra de voter pour une liste d’universités disposées en ordre de préférence. 

Le gagnant sera ensuite nommé par un ordinateur. Cette méthode a été choisie car elle est intéres- 

sante dn point de vue mathématique, elle est moderne, elle satisfait une grande partie des critères 

d’un vote (critère de Condorcet, critère de majorité, indépendance des clônes, etc.), et elle a été 

adoptée par des organisations reconnues comme la fondation Wikimedia. L’université gagnante sera 

annoncée au banquet de clôture du congrès.


4.7 Sponsors / Commanditaires 

Official Sponsor / Partenaire Officiel 

Welcome to Kelowna, and to 

UBC’s Okanagan campus. 

PROFESSOR WESLEY PUE 

Provost and Vice Principal 

UBC’s Okanagan campus 

The University of British Columbia is very proud to host so many outstanding 

undergraduate researchers at the 2012 Canadian Undergraduate Mathematics 

Conference. We encourage you to get to know our Okanagan campus and the many 

advantages of pursuing your studies here at UBC. 

Our Okanagan campus offers a diverse range of thesis-based interdisciplinary graduate 

studies — from the humanities and creative arts to social and natural sciences. 

Learn. Share. Enjoy. We look forward to welcoming you again as you prepare for an 

exciting future in whichever fields of endeavour your passion for mathematics takes you.

4.7. SPONSORS / COMMANDITAIRES 75 

Okanagan College is pleased to welcome the 

participants of the Canadian Undergraduate 

Mathematics Conference. With four campuses spread 

throughout the Okanagan Valley, the College offers a broad range 

of career, continuing education, degree, developmental, trades and 

technologies, university studies, and vocational programs – including 

a Mathematics and Statistics Department that offers a wide variety of 

first- and second-year courses in mathematics and statistics that are 

eligible for transfer to post-secondary institutions across Canada. 

The College’s participation in this conference has been sponsored 

and supported by the Science, Technology and Health and Social 

Development portfolio, the Okanagan College Faculty Association 

(OCFA), the Applied Science Technologists and Technicians of British 

Columbia (ASTTBC) and the British Columbia Women in Technology 

(BCWIT). 

The Science, Technology and Health and Social Development portfolio 

includes 17 different programs that serve more than 1,000 students at 

all four of Okanagan College’s regional campuses. The portfolio acts 

as a stepping stone for a wide variety of careers and for further postsecondary 

education. 

The OCFA represents more than 200 faculty members of Okanagan 

College. It serves to maintain and promote the professional status of 

the members of the Association, to regulate relations between faculty 

and Okanagan College through collective bargaining, and to function 

as a trade union pursuant to the laws of British Columbia. 

ASTTBC is the professional association that governs applied science 

technologists, certified technicians and a number of technical 

specialists and is charged with regulating the standards of training 

and practice of and for its members and protecting the interests of the 

public. With more than 10,000 registrants, ASTTBC is one of the larger 

professional associations in B.C. and maintains high academic, and 

professional practice standards. 

The BCWIT focuses on raising the profile of women working in 

technology to capture the interest of girls at a younger age through 

hands on events, and focused career counselling. The organization was 

established following a survey by ASTTBC which revealed only nine 

percent of its members are women. 

Okanagan College 

Science, Technology, 

and Health and 

Social Development


THE IRVING K. BARBER 

SCHOOL OF ARTS AND SCIENCES 

Be here 

Be inspired 

Study hard 

Focus 

Optimize 

Connect 

Have fun 

Imagine 

Philosophize 

Compute 

Connect 

Set goals 

Achieve goals 

Calculate 

Explore 

Research 

Collaborate 

Be remarkable 

54 undergraduate 

programs 

7graduate 

programs 

1 

exceptional 

learning 

experience 

GET INSPIRED 

www.ubc.ca/okanagan/ikbarberschool

4.7. SPONSORS / COMMANDITAIRES 77 

Silver Sponsor / Partenaire Argent 

Pacific Institute for the Mathematical Sciences 

Bronze Sponsor / Partenaire Bronze 

Canadian Mathematical 

Society 

Westcoast Women in 

Engineering, Science 

& Technology 

Applied Science 

Technologists & 

Technicians of BC 

Centre de Recherche 

Mathématiques 

CMS Women in Math 

Committee


Contributors / Contributeurs 

Golden Key 

International Honour 

Society 

Department of 

Mathematics and 

Statistics, UNBC 

The Canadian Society for 

History and Philosophy 

of Mathematics 

4.8 Riddles and Games / Énigmes et Jeux 

Crates of Fruit 

UBC’s Okanagan 

Campus AVP Students 

You are on an island and there are three crates of fruit that have washed up in front of you. One 

crate contains only apples. One crate contains only oranges. The other crate contains both apples 

and oranges. 

Each crate is labeled. One reads “apples”, one reads “oranges”, and one reads “apples and 

oranges”. You know that NONE of the crates have been labeled correctly - they are all wrong. 

If you can only take out and look at just one of the pieces of fruit from just one of the crates, 

how can you label ALL of the crates correctly? 

Explain Elevator 

A Man works on the 10th floor and always takes the elevator down to ground level at the end of 

the day. Yet every morning he only takes the elevator to the 7th floor and walks up the stairs to 

the 10th floor, even when is in a hurry. Why? 

Five Gears 

There are five gears connected in a row, the first one is connected to the second one, the second 

one is connected to the third one, and so on. 

How much faster would the last gear be if the second gear was twice the size of the first gear, 

and all the other gears were the same size as the first gear?

4.8. RIDDLES AND GAMES / ÉNIGMES ET JEUX 79 

Rope Burning Puzzle 

There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily 

of the same length or width as each other. They also are not of uniform width (may be wider in 

middle than on the end), thus burning half of the rope is not necessarily 1/2 hour. 

By burning the ropes, how do you measure exactly 45 minutes worth of time?


33333 puzzle 

Use each of the numbers one through nine exactly once to fill in the blacks and complete this 

equation. 

�� − �� = 33333 

The Emperor 

You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The 

celebration is the most important party you have ever hosted. You’ve got 1000 bottles of wine you 

were planning to open for the celebration, but you find out that one of them is poisoned. 

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after 

consuming even the minutest amount of poison. 

You have over a thousand slaves at your disposal and just under 24 hours to determine which 

single bottle is poisoned. 

You have a handful of prisoners about to be executed, and it would mar your celebration to 

have anyone else killed. 

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely 

sure to find the poisoned bottle within 24 hours? 

The Card Trick 

I ask Alex to pick any 5 cards out of a deck with no Jokers. 

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then 

hands them to me (Peter can’t see any of this). I look at the cards and I pick 1 card out and give 

it back to Alex. I then arrange the other four cards in a special way, and give those 4 cards all face 

down, and in a neat pile, to Peter. 

Peter looks at the 4 cards i gave him, and says out loud which card Alex is holding (suit and 

number). How? 

The solution uses pure logic, not sleight of hand. All Peter needs to know is the order of the 

cards and what is on their face, nothing more. 

4.9 Campus Maps / Cartes du campus 

See next page

4.9. CAMPUS MAPS / CARTES DU CAMPUS 81

82 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES

4.9. CAMPUS MAPS / CARTES DU CAMPUS 83

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